Class 9th Physics & Chemistry AP Board Solution
Improve Your Learning- As shown in figure 23, a point traverses the curved path. Draw the displacement vector…
- “She moves at a constant speed in a constant direction.”. Rephrase the same sentence in…
- What is the average speed of a Cheetah that sprints 100m in 4sec.? What if it sprints 50m…
- Correct your friend who says, “The car rounded the curve at a constant velocity of 70…
- Suppose that the three ball’s shown in figure start simultaneously from the tops of the…
- Distance vs time graphs showing motion of two cars A and B are given. Which car moves…
- Draw the distance vs time graph when the speed of a body increases uniformly.…
- Draw the distance - time graph when its speed decreases uniformly.…
- A car travels at a velocity of 80 km/h during the first half of its running time and at 40…
- A car covers half the distance at a speed of 50 km/h and the other half at 40km/h. Find…
- Derive the equation for uniform accelerated motion for the displacement covered in its nth…
- A particle covers 10m in first 5s and 10m in next 3s. Assuming constant acceleration. Find…
- A car starts from rest and travels with uniform acceleration “α” for some time and then…
- A man is 48m behind a bus which is at rest. The bus starts accelerating at the rate of 1…
- A body leaving a certain point “O” moves with a constant acceleration. At the end of the…
- Distinguish between speed and velocity.
- What do you mean by constant acceleration?
- When the velocity is constant, can the average velocity over any time interval differ from…
- Can the direction of velocity of an object reverse when it’s acceleration is constant? If…
- A point mass starts moving in a straight line with constant acceleration “a”.…
- Consider a train which can accelerate with an acceleration of 20cm/s^2 and slow down with…
- You may have heard the story of the race between the rabbit and tortoise. They started…
- A train of length 50m is moving with a constant speed of 10m/s. Calculate the time taken…
- Two trains, each having a speed of 30km/h, are headed at each other on the same track. A…
- As shown in figure 23, a point traverses the curved path. Draw the displacement vector…
- “She moves at a constant speed in a constant direction.”. Rephrase the same sentence in…
- What is the average speed of a Cheetah that sprints 100m in 4sec.? What if it sprints 50m…
- Correct your friend who says, “The car rounded the curve at a constant velocity of 70…
- Suppose that the three ball’s shown in figure start simultaneously from the tops of the…
- Distance vs time graphs showing motion of two cars A and B are given. Which car moves…
- Draw the distance vs time graph when the speed of a body increases uniformly.…
- Draw the distance - time graph when its speed decreases uniformly.…
- A car travels at a velocity of 80 km/h during the first half of its running time and at 40…
- A car covers half the distance at a speed of 50 km/h and the other half at 40km/h. Find…
- Derive the equation for uniform accelerated motion for the displacement covered in its nth…
- A particle covers 10m in first 5s and 10m in next 3s. Assuming constant acceleration. Find…
- A car starts from rest and travels with uniform acceleration “α” for some time and then…
- A man is 48m behind a bus which is at rest. The bus starts accelerating at the rate of 1…
- A body leaving a certain point “O” moves with a constant acceleration. At the end of the…
- Distinguish between speed and velocity.
- What do you mean by constant acceleration?
- When the velocity is constant, can the average velocity over any time interval differ from…
- Can the direction of velocity of an object reverse when it’s acceleration is constant? If…
- A point mass starts moving in a straight line with constant acceleration “a”.…
- Consider a train which can accelerate with an acceleration of 20cm/s^2 and slow down with…
- You may have heard the story of the race between the rabbit and tortoise. They started…
- A train of length 50m is moving with a constant speed of 10m/s. Calculate the time taken…
- Two trains, each having a speed of 30km/h, are headed at each other on the same track. A…
Improve Your Learning
Question 1.As shown in figure 23, a point traverses the curved path. Draw the displacement vector from given points A to B
![](data:image/jpeg;base64,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)
Answer:![](data:image/png;base64,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)
Displacement is shortest distance between initial point to final point and its direction will be from A to B. So it will be a straight line from point A to point B.
Question 2.“She moves at a constant speed in a constant direction.”. Rephrase the same sentence in fewer words using concepts related to motion.
Answer:Sentence can be rephrased as “She moves at constant velocity.” or you can also write it as “She moves at zero acceleration.” as there is no change in its speed or direction resulting in no change in velocity.
Question 3.What is the average speed of a Cheetah that sprints 100m in 4sec.? What if it sprints 50m in 2sec?
Answer:Given, distance = 100m and time = 4sec.
Using formula, ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
If distance = 50m and time = 2 sec, then
![](data:image/png;base64,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)
= 25 m/s
So speed remains same for both the cases.
Question 4.Correct your friend who says, “The car rounded the curve at a constant velocity of 70 km/h”.
Answer:Correct statement will be: “The car rounded the curve at a constant speed of 70 km/h.”
Explanation:
Because velocity denotes speed (magnitude) with direction. And, we know that in circular motion, the direction changes, as shown below:
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADJAIwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAqpd6pY2FxaW93dRQzXcnlwI7YMjYzgfoPqQOpGbdcf4o8K6Nquu6TcX1o00tzcmCUtPIAYxBKwUANhRuUHjHOfU5io5Je6dOEp0alS1ZtKzeiTeiv1a/r7zsKK4fUvGt3oV5eab/ZEUj2fkrbpJqD+deK52qYw0ZLkfxcnBzya7WIyGFDMipKVG9UbcoPcAkDI98D6URqRk2l0CvhKtCMZzWkttVron0b6ND6KKKs5gooooAKKKKACiiigAooooAKKKKACiiigArI1j/kJ6B/1/t/6TT1r1kax/wAhPQP+v9v/AEmnqZ7fd+Zvh/jfpL/0li3/AIc07Utc07V7iPN1YbvL+VcNnpuyMnaeV5GCc1rUVxfj74maL4At41vBJdahOjNBZQkbiADhnJ+4hYYzyeuAcHDUUrtdSJ1ZzUYyd0tF5dTsJ54bW3luLiWOGCJC8kkjBVRQMkkngADvXn+v/G3wRoLtEuoSanOrhWj05BKACud28kIR0BwxOTjHBxy8Xw98X/E14NV8e6rJpmnuiPFotiCpT5WALK+Qj8g5O9sMVO3AA9Q0Dwd4c8LIq6Lo9paOEKecqbpWUtuIaRsuwzjgk9B6CmZnni/GrVtQYXOh/DnXdR0qQ/ursK4LgcNwkbrwwYcMenboFvvjVq2mWcl5f/DnXrS1jxvmnVo0XJAGWMeBkkD8a9eopNN9TSE4x3in63/Ro8l0D466TrzrE0en6ZOzlVj1G+eIEBc7t4hKAdQMsDkYxyM+gQahrd1bxXFvYaRNBKgeOSPVHZXUjIIIgwQR3puv+DvDnilGXWtHtLtygTzmTbKqhtwCyLh1Gc8AjqfU15hL8PPF/wAMpJ9V8A6rJqenojvLot8Cxf5VBKqmA78E5GxsKFG7JBXK+/5F+2h/z7X/AJN/meq/aPEP/QL0v/wZSf8Axij7R4h/6Bel/wDgyk/+MVg+AfiZovj+3kWzElrqECK09lMRuAIGWQj76BjjPB6ZAyM9pRyvv+Qe2h/z7X/k3+Zk/aPEP/QL0v8A8GUn/wAYrD8X6h4ntvDNzNb2drbzrJD5clrePLJuMqAAIYgGyeMZ5BPXpTPiAbnTIbTX4nvJLW0Yx3lpBeyW6yI3CNlW4KuR0BJ3c8Ctzwrp17pnh21g1K6nub5l8y4eeUyMHPO3JY8LwODg4z3rF80pOnd/18v6sejBUqNKni+WL1216br4ntp0t7y31te0uS+l0u2k1OCKC+aMGaKJ9yq3fB//AF46ZPU26KK3SsjyZS5pN2sFFFFMkKyNY/5Cegf9f7f+k09a9ZGsf8hPQP8Ar/b/ANJp6me33fmb4f436S/9JZnfEDxjb+B/CVzq0vzXDfubOMoWEk5UlA2CMLwSeRwDjnAPL/C3wLcW27xp4qE9x4q1HdIxulAa1Q8ABf4WK49NqkIAuGzh2aTfEj49XVzOJBovhF/LjjYkZuFYgHAfgmRWbcBgrEgYc17ZVGAUUUUAFFFFABRRRQB5f8UvAtxc7fGfhUT2/irTtsim1UFrpBwQV/iYLn13KChDZXHUfD/xjb+OPCVtq0Xy3C/ubyMIVEc4UFwuScryCOTwRnnIHUV4neJN8N/j1a3UAkOi+Ln8uSNSTi4ZgCcF+SJGVtxGAsrhRxQB7ZRRRQAUUUUAFFFFABXK+PNSm0fSbfVLdY2nsmubiNZASpZLO4YA4IOMj1FdVXlP7Qn/ACTRf+v+L+T1M9vu/M3w/wAb9Jf+kstfAbTYbH4V2dxE0he/uJriUMRgMHMWF46bY1655J+lemVz/gT/AJJ54Z/7BVr/AOilroKowCiiigAooooAKKKKACvM/jzpsN98K7y4laQPYXENxEFIwWLiLDcdNsjdMcgfSvTK5/x3/wAk98S/9gq6/wDRTUAXPDWpTaz4V0fVLhY1nvbKG4kWMEKGdAxAyScZPqa1K4L4LRtF8I9CVxglZm69jNIR+hrvaBtNOzCiiigQUUUUAFcZ8V9Hj1v4Y67A7KjQWxu0do95UxfvMD0JClc9gx69K7Oo54Ibq3lt7iKOaCVCkkcihldSMEEHggjtQCdjk/hXqf8Aa/wv8PXPk+VstBbbd27PlExbs4HXZnHbOOetdhXj/wAFr59D1HxF8Pr6SdrrSruSa1eZWXzICQpKochFztcfNz52R3J9goAKKKKACiiigAooooAK4/4qan/ZHwv8Q3Pk+bvtDbbd23HmkRbs4PTfnHfGOOtdhXkHxpvpNc1Dw78PrGSdbrVbuOa6eFWby4ASoLIMB1zuc/Nx5OT2IAOo+EP/ACSnQP8Ari3/AKMau3rE8KQQ2uhtb28UcMEV5dpHHGoVUUXEgAAHAAHatuph8KN8V/Hn6v8AMKKKKowCiiigAoqvf31vptjNe3TMtvCu6RljZyo7nCgnA78cDms6w8VaRqV9DZWs07XE0Pnxq1pMgaPs+WUDaexzgnipcop2bNYUKs4OcYtpbuzseefFPw9d6H4g034maDbyTXmmOo1G2iRB5tuAwZycE52koThiFIPAQmvSPDmv2Pinw/Z61prSG0ukLJ5ibWUglWUj1DAjjI44JHNaE8EN1by29xFHNBKhSSORQyupGCCDwQR2rxS/0vxB8FdYudT8N2U+seD7vdLcadvYtZuFJ3bsMVUAffwflG1+QrGjI9vorD8L+LtF8YaWl/o97HMCitLAWAlgJz8si5ypyrexxkEjmtygAooooAKKKw/FHi7RfB+lvf6xexwgIzRQBgZZyMfLGucscsvsM5JA5oAseItfsfC3h+81rUmkFpaoGfy03MxJCqoHqWIHOBzyQOa83+Fnh+713xBqXxM162khvNSdhp1tKiHyrchQrg4BztAQHCkqCeQ4NZdhpniD416xban4ksp9H8H2m2W307ewa8cqDu3YUspB+/gYU7U5LMPbIIIbW3it7eKOGCJAkccahVRQMAADgADtQBmeHP8AkGTf9f8Aef8ApTJWvWR4c/5Bk3/X/ef+lMla9TD4Ub4r+PP1f5hRRRVGAUyWWOCF5ppFjijUs7ucKoHJJJ6Cn0UAvM5XTvHHhzXLa9E95ZwWwma3VLyZEM6bRltjfwnJGD2HOOQMnwgmheHZr2a78Uaddys3kWjyagkjRWq8omTjaeTkD5eBiuv0jRLHQ0uo9Pi8mG4nNw0Q+6jFVBCjsPlzjtk44wBo1gqcnaUrXR6c8XQgp0qClySt1XT5P5mT/wAJT4e/6D2l/wDgZH/jR/wlPh7/AKD2l/8AgZH/AI1rUVraXf8Ar7zj5qH8r+9f/Iniviv4f+D76/OteEvFmn+HNYRMR/ZLuOOAnay8BCDGWyAWXjGflJJNU/8AhaPjjwh+61y10TxNar+7W70y9QSSO3zAkJkhQMr/AKpeQOf73u1FFpd/6+8Oah/K/vX/AMieQ2P7QGlSWcbX/hnXoLo53xwQrKg5OMMWUnjH8I/HrSyfH7S7mQ2Wi+GNev8AVm/1Vm0KoX7n7rOwwuTwp6duo9doprm6kTdNr3E16u/6I8f/AOEo+LXi/wDdaH4Xg8M2rfu2u9TJMkbr8xIDqCVIwv8Aqm5J5/u3PCnwWsbG/GteLb6TxHrDpiT7X+8gB2KvIfJkK4IDNgYI+UEA16pRTMwoqpqlk2o6Xc2kdzLbSSxlUniZlaNuzAqQeDg4zz0PBrh/ASanqGqT3d9Jfwx6bH9hlgl1CSdZrpf9ZIQWwMDA24K/NkHIrOVRqSjbc7KOFjUoTrOVuXp67der+7qdZ4c/5Bk3/X/ef+lMla9ZHhz/AJBk3/X/AHn/AKUyVr1UPhRliv48/V/mFFFFUYBRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABVe/umsrGa6W1nujEu7ybdQZGHfaCRk+2cntk8VYooY4tJptXOP8B+I4Ncs7pLWyvEijubiUzyoojzJMzqgIYkttcZ4wPXkZ7CmRxRwqVijVFLMxCrgZJJJ+pJJPuafUQi4xSbub4qrCrWlUpx5U+l7hRRRVnOFFFFAHJX/inWrLWYNN/4R2JpLuS4W03agAZliXdu4QhdwPAJ69cDmptJ8YLc6zeaTq0Nrpd9B5ASJr1XMrSLu2rkLkjIBxnk/TMur6RqN54t0LU7dbX7Lp3m+YJJmV28xdpwAhHAGevPTjrXPa74L1nVLzxHLFFpY/tbyEile4ffCkRX/pn/ABbVJAPGB1xXLJ1Ytta6/hb07nu0aeBqwjGaUW46tN3Uue2zk18Gtvu1O4/tXTv7R/s/7fa/bv8An285fM6bvu5z05+lZPizxZb+GNOafNrPdLtb7I90IpHQnbuUYJPPt0B54xWFZeCtSi1yS5uhYS2smpjUhm5uCYXOSwWMFUYhsAOewJIOdoPE3g3WdSuNdGnTWHkax9mMpuGdWi8kdAFUg5IU5J9RjvTlOryOy1Io4XALEQU6l42TfRPVXV1tpd99LdUdFH4nshqOpQ3dzYW1raSRxJcNfRnzHYEsrLnKEFSMHrg+lWIvEmhTzJDDrWnSSyMFREukLMTwAADya5DVvCPiHVP+Ei/d6XF/bP2b/l7kbyfJx/0yG7OPbHvTr/wLfXWrXkyRad9hv4bZZbZp50SAxhVwFjKiVQAcbtvOPu4OV7Sr0X9a/wDA+8r6pgGk5VLaLZp9I3/Fy6293S10dFrHjPQtFtLiabUIJ5bdtr21vMjTZ3BSNpYcjv6YNTaf4ittQu9T2S2ZsbJUZbuK9jkVwVJYsAf3YXBHzdcE9q5IeBNVHg670Ax6S8oXy7XUNzLKY/PEuxxsOB948MRnAx/FRqvgrXdV1PUL910lGuLm1ukgkleWMmFSmx/3a5VgxJ+mMc5A6la97f1r/wAAuODy9xcfaa3erfS8bNLTdc297a31sdkfEmhCFZjrWnCJmKq5uk2kjBIBz1G4fmPWr1tdW97brcWlxFcQPnbJE4ZWwcHBHHUGvP77wJqt3fSXxj0lmutRhvbi03MsQEW8BM7DvLh8sxVec8HPG5p3hq9i07xPp9zLAkWrXNxNDLExdkEo2/MpA5GAeCc5PTHNxqVG7OJzV8Jg401KnV10v+F/u/G11ual74m0ayt76V9RtZHso2eaGOdDIu04I2567iFwcckCsuPxxZReEf8AhIL4QLEWRRBZ3ImfLBTsOQuHGSSvYAmsA+A9ZmsLNJBo0E9hYS2cX2cOPP8ANV0LO23K4DbsANli/I3cbmo+G9R1D4bJ4e3Wsd8sEMO7zGMZ8tl5ztzyF9Opx71HPWd3a2hu8Pl9Nwi5815JN32V9fw1v0vbdMsad4xsrvX7/SriSzt2gaH7LILsMLsSjcpQEDnBXgZ5br3O1/aunf2j/Z/2+1+3f8+3nL5nTd93OenP0rhNX8Ga7q03iCY2+kxy6stuqubp2aAR7SQD5XIbaPToOuKsWXgrUotckuboWEtrJqY1IZubgmFzksFjBVGIbADnsCSDnaCNSre1r/8ADsVXCYBx51UtotE09eWN+vdvTy00sd9RRRXUeGFFVNU0231fS7nT7td0FxGUbgEjPQjIIyDgg9iBXmEPw/1qTRtTaWysLXUYrRLGyFqwQTqrZkkY/wB91+XJK5BYMADWVSpKL0jc9DB4ShXi3Uq8jTS1XfrutuvZano2r65Bo02npcW87rfXK2qSRBSqO33d2WBweeQD0PtnUry4eGtYhFnJb6JeIq6pa3ssBurXaoiQhyqIERSSwAIyW2Zbbxmt/wAIX4lurO3iW2+ya7b3Ejya7JqDEzpgKoBXL8rgYIGAnq5FZe2nf4X/AF8jueWYVxS9vFd3dP8ADm2W2l3tpuen39/9h+zf6JdXHnzrB/o8e/y92fnf0QY5Paiw1Oz1P7T9jm8z7LO1tN8pG2Rcbl5HOMjkcV5tF4UuobPQ5YPCEtvqdpd20t5MlxARIkQIO395wW4YjAyepOM1R1vw1LoWk6pq50azjks9Ya4gM6RvFNaSHYI9gJ4B2nDAbQflIOaTr1Fq46fP/IqGVYWbVONb3m7L4dXe2yk9O1ntrY9ioriovA0Enw1TQGhWK8aETF325W5xnJYA8A/JkZO3jNc7J4H1mXRZ9Q/sqzt9UuL2F5dPtGjjj+zxjGxchkyzYcgllO1TjIxWkqs1b3en9dDlpYDC1HJe3StKyulr2fxbb+Stq9T1eqlhqdnqf2n7HN5n2Wdrab5SNsi43LyOcZHI4rzaDwZepqaNfaFdahosscyLZPfReZasZA+9VXYibto+VG4BOT2JH4R1W01SRl0HztMOrTTTWkc8ca3Nu20w/LuAYRlS2xsD5gB1bEe2qfy/n/kbLLMLZr26vuvht6fFv9y21tqeqUV5RY+BL6PVtG+36GsunxXM0zxLcJItvFIFMcJLMC4RwzEAEHcSNxYitTx34Z1jULq1fRbPMdtaCO1+zypGYJRKjdHICDavDR4bIwTtwKr20+Vy5dv67Gby7De2hSVdWlfXSy1a197fr8+p3FvqdndajeWEM266s9n2hNpGzeMryRg5HpmrdcloGjz2njXXdTk0n7NBfRwvBL+6yp2jzFO1iQSxyccEqTnpnm9D8CX8s32bXLOfJW5jubxbmApOH+62Ahkkbcdw8w/KUDDn5Q/az093v+ZP1HDNyftUklF9G23G7tqtnpbc9RoryWH4f61Jo2ptLZWFrqMVoljZC1YIJ1VsySMf77r8uSVyCwYAGi68F31xBAD4dujG1/DNPC11bDbGqYlCLGI1TdlRwct5YLbSBmPbz/k/r7jZZXhb2+sLT08npeWu/wB6PWqK8om8KQf8LPXRk0+z/sp2TVSEjXfGqqVKEsPuNJjKDIwRjHNer1rTm53urWOHG4Wnh1Dknzcyvta1/m9e4yWWOCF5ppFjijUs7ucKoHJJJ6CiKWOeFJoZFkikUMjo2VYHkEEdRWT4tnFt4R1abz1gKWzlWdUZWOOFIcFSGOFwRzuwOa8+XxPqDmCHT/EcUMMPh4XrQQxW5H2hIzmJRt+XpuK8kAEDAxhVKyhKzNcHlk8VSdSDSs+t+3kmetUV5dD4x1TWNb063t9ZWJLpbZWh02BJXjdkDSBxIOnLfOrMECYZcmud03xXqeg+EtMXTr9RHFDLM0UqJtZ/tCjygcEsdrbig2sA+7cRhRm8XBdNDshw9iJK3MlJ2016p7u3l/wdr+51R1DSLHVJrOW8iaRrOYTwASuqq46MQCASPfPU+prznVPF+pw3/iS607xFFcWmm/Z5bW3CQuswkZA43KMlFyV4OeRls9dzwxJE/wARvFTJqHnCWO1ljXchEiGPIYYGSFBABHZhnJINV7eM3y26/wCf+Rg8rr4em6/Payvpe+vJpsraTXfqu9uygure6837PcRTeVIYpPLcNscdVOOhHpRPdW9r5X2i4ih82QRR+Y4Xe56KM9SfSvI/+EvubG2vYrPW7OM/2rds0kUUInniVV2yDCCNicsx3bS+0KrZrp/E2qPZ6b4Qnu7xUlkvbYzreW8SMRgF5CrA+Wy+qkbd556UliYuLfYqpktWnUjFvSV7b30V+x3dFeV2ni/U4bhryTxFFdWcevLp5jkSEL9mIb96zKAeQMgjA+U9RwNT4geKdW8P6hCLCdYYktvP2yxqFnbzUUoGIJc7ScquwgHduPSn9ZhyuXYj+xcR7eNBNXltvbTpqv0O9lljgheaaRY4o1LO7nCqBySSegqvDqunXH2byb+1k+1bvs+yZT5u3723B+bHfHSud8U6/JY3OiNHqP2PSLvznuL+FVfAWPdGFZgy/NzgYJOOK4fwxq9rbW/g+B9WtYE8u+S4L+QWtSS5RgzqShbcOpwcDg85U8Qoz5f66f5lYbKJ1cP7Z+dt+invpveO3n0uj2WivILTxV4hbS9C1CfxDmG/uJ4bljHDFHbsuPLVnET7SeWyR0I6AFq0dE8Ra1q2qJYaj4li02Ty7d7Z4rMKt/G2QzL5yA7ySoBAxwcKRQsVBtKz/D/MqpkNenGUnKNle/xdHZ/Zvuvu12PSJLq3iuIbeS4iSefd5UbOA0m0ZO0dTgdcVNXiWga0+m6b4Z+yXsF1crDfkWcscTtDJhvLVcL5imRiON2WyAPStN/GOsSWcV7aa/58cthNPeBLNFSwmwzRJuKn7zL5YDEk8kcspExxcWrtf1p/ma1eH60Z8sJK2urv0cl2dvh+b2bPTLPSLGwvr29t4mW5vWVriRpXcuVzj7xOAMkADAxx2FXq4Hwl4jv59bsLG/1eK+S/0lb1WKRoVm3sDGm3GcKDkHJyhPHIrvq3pTjKN4qx5eOw9WhV5asru2+u23Wz0tYKKKZKZBC5hRXlCnYrttUnsCQDge+D9K0ONK4+ivMNM+JN5Y+HdPuNWtPtkksbzTTxyAN5QmEYOxVwDkn721TtGGLEgbWpeO7rTNR1iGbRVez0loftFxHd/MVlKhNqFBlsNnGQOCN3TOCxNNq9/wCtz1Z5LjIzcOVPVrda2ajpdrq0u+ux2tFcVf8AxDj06/uoZtNdora5e3eNJs3RCxlzKISP9Vx97d059qrS/ES9h0aTU38OS+QkEVwJDJIsZV2C7d7RAFwWU4GVIyQ3GC3iKa6kRyjGSSahva2q67dTvqK8/wBf8Z6tH4d1wQ2a6dqumNbed++WZUWXaRglMM3JUjGB1DGtbxbq2saZDoJslgjlutRhguFMmVO7P7sEoflPPz4BGBgc8Ht46+X/AAwllle8U7JybS1XRKV9NLNNWOqorjLbx49z/Zd4ujSrpGpXYs4Llp18wOeAWjHQFgw+90UnHQGp4p1bV18QatpkcvlWMegy3ieVMUdXUnEgZVDZ3ALt3YI5P92h14Wuhwyuu6ns52W73XR2e3VdtGd9RXnlh4+m0vw9ENW06U3EOkw3sbLcCQ3ClxEC5IG0sxVv4uGOeRg9DY+J5ZbDVbq/0m6tE0+PzS2x9sybSx2eYiEkYIIIHbnmnGvCXUmtlmJpXbjona91rttr5o6KiuBvPEmqXkeg3F1pUtjZ3d/aGGa11PmXzFLBWXy8lAPvKcZOMEjmnjx7qRmZP7AgCjVBpIkOoHa0xz0/d52jA5I7jAPOF9Yh1/Jl/wBk4lq8Un/29H/P/hju6K82vPFF9oniW61LU7S6twui+fJpgvPNQSm4ESkHO0ZG3JA4yeCc57DQdbudWa7S60ueyaBl2u6SCOYMM5UyIjZBBBG305OacK0ZPl6meIy6tRp+13j3ut9NN9d1qvU2aKKK1OAKKKKAObPgHw0bRbX+z28lVKBRcy/dLBtpO7JXcA208A5IGSalfwZoUi3iy208ovVRbnzbyZzKFIK5JfqMDB6gcdCa36Kz9lT/AJV9x1/X8V/z9l979e/dXPM9S8K65Jd6w9rDeJe3VzCsFxHdqbVrdFVAJ1di8h2lt2VbJHHBOenHgHw0LRrX+z28llCFTcy/dDFtoO7IXcS20cE4JGQK6WipjQgm3a5vVzXFTjGKly27Nq9kkr69Ladte5hz+ENEuftnn2ssn2yOOO53XUp80R7dm75uSNo+br155Obd/odhqdnbWt5HLJHayLLCfPkDq6ghW3htxIyeSffrWjRWnJHscjxVdtPnem2r00tp8kl6GHaeDvD9jeC6t9MiWRZGlQMzMkbkglkQkqh+VeVAxgDpU2peGtK1a8a7vIJWnaD7MzR3Mke6IkkoQjAEEk8Gtail7OFrWH9bxDlz87v3u7nO/wDCDeHj9+ylkHkfZtst3M4EXZMM5GAeQOxAIwQDV7T/AA7pOl21xb2tmoiuFCTCVmlMihdoUlySVC8BegHbmtSihU4J3SCeMxE1yzqNr1Zzq+B9AS3gt1t7pYLeQSwxi/nCxuCSGUb8A5J5HqaefBegNY3NlJYtLb3MwnlWW4lcmT++CzEhj3IIJHBzW/RR7KHZFPHYp/8ALyXfd77/AJmBL4M0K4meW5tp7iSSEwM1xeTSZjPO35nPAPI9CARggGnweD9Bt0iSOx/1U8VwjNM7MHjXbH8xbJCjgKTgelblFHs4dkJ43EtW9pK3qwoooqzmP//Z)
So velocity will not remain constant but speed will remain constant.
Question 5.Suppose that the three ball’s shown in figure start simultaneously from the tops of the hills. Which one reaches the bottom first? Explain. See figure 24.
![](data:image/png;base64,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)
Answer:First ball will reach the bottom first because all the balls will have same initial speed but path covered by the first ball is the shortest one i.e. straight line between top of the hill and bottom.
So, as distance is shorter and initial speed is same, so first ball will take less time than other two balls.
Question 6.Distance vs time graphs showing motion of two cars A and B are given. Which car moves fast? See figure 25.
![](data:image/png;base64,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)
Answer:Car A moves faster than car B because slope of s-t graph denotes speed.
Here slope of A is greater than slope of B so car A is moving with faster speed than car B.
Question 7.Draw the distance vs time graph when the speed of a body increases uniformly.
Answer:![](data:image/jpeg;base64,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)
Slope of Distance-time graph denotes speed and change in slope of the graph is acceleration. So it must be constant and positive for this graph as speed is increasing.
Question 8.Draw the distance – time graph when its speed decreases uniformly.
Answer:![](data:image/jpeg;base64,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)
Slope of Distance-time graph denotes speed and change in slope of the graph is acceleration. So it must be constant and negative for this graph as speed is decreasing.
Question 9.A car travels at a velocity of 80 km/h during the first half of its running time and at 40 km/h during the other half. Find the average speed of the car.
Answer:Let the total running time be t h.
Distance covered in first
h![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Distance covered in other
h![](data:image/png;base64,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)
![](data:image/png;base64,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)
Total distance![](data:image/png;base64,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)
So, Average speed![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG0AAAAjCAMAAACpdHR4AAAAAXNSR0IArs4c6QAAAIpQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OgBmOjo6OmaQOma2OpDbZgAAZjoAZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkLb/kNv/tmYAtmY6tmaQtpA6tpBmtv//25A625Bm27Zm29u229vb2////7Zm/7aQ/9uQ/9u2//+2///bmbj0VwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB3klEQVRYR+2WgVKCQBCGd0kDS8VUKlNTyIIQ3v/1+vcO8CgFKWZwJm+G4c7d2739Z/E+ouvoToGA7Ty5mgb9sIXDBEVQBDMXq4NBpodspR0NT2AEJTIXRtBy/NKOZtk2zNwP9xPmYUjZ4pl5XNQpJigZwYveHOap6YRft441J0qxp+9T8sg8qjqAnDT17HDvYiKLxJ3RGqF1QWJKn7SS8WBOwbjsZC1o1Q/FK77zU29Me7cuWzxYItyNXygZFdm0SWdLPesBrZIrqZz0o7yIYtTOfF42bFSBdvciblabmY3ofQLZSk7lbDppxYAOH4kLJT1REovIWlLQ82l9Ky2fuCOYMEUFKEa0Mp2y2iRA+hqq17YqW+xYU4rRCiMEl0XicW/LdqRahShyeLjhKSyLTwiFYxhOkM7GM5YAPdSFlzVr1qZX78tSYCUfgxroum5GcYL2Jl0UcgFKdlH2P85pMEpbgPINS44xirpg28EhBKpjlD8Qyc/OqGMUZd/hptU4stiw9YIbsI5FTrVgDaPo2tUFiv++lTw2wEVYBCDUeEi0CkYxsuVIYmcsoi7ehuOQ7SijHM9WyyInlaxmFEUkOWapN9hFs8hvLpU6RhG7AIrgiHCLYpcrizTsoPPdvwDXqDeQBCCu7wAAAABJRU5ErkJggg==)
60 km/h
Question 10.A car covers half the distance at a speed of 50 km/h and the other half at 40km/h. Find the average speed of the car.
Answer:Let the total distance covered by the car be ‘d’ km.
Time taken to cover first
distance, t1![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Time taken to cover second
distance, t2![](data:image/png;base64,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)
![](data:image/png;base64,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)
Total time = t1 + t2
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Therefore, average speed![](data:image/png;base64,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)
= 44.44 km/h
Question 11.Derive the equation for uniform accelerated motion for the displacement covered in its nth second of its motion.
Answer:Let the total displacement covered after n sec = Sn
Let the initial velocity be u and acceleration be a.
Displacement covered in nth sec = Sn – Sn-1
From the equation of motion, we know that![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH4AAAAhCAMAAAAoJe+YAAAAAXNSR0IArs4c6QAAAJBQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OjoAOjpmOjqQOmZmOmaQOma2OpDbZgAAZgA6ZjoAZjo6ZmY6ZpC2ZrbbZrb/kDoAkDo6kGYAkLbbkNv/tmYAtmY6tmZmttvbtv//25A625Bm27Zm27aQ29uQ29u22/+22////7Zm/9uQ/9u2//+2///by5nBogAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABf0lEQVRYR+1Vf1ODMAxNp3P1J8NNHVOZikyFQr//t7PpnJYDmg7o7byjf/WOvLzmvYQAjMeLAnIz85LXLen79eKY9ADJSN/m1OeCscDNxo5RNvHL2ydIJ88dM7vAZHyWWePEuUf6hKkzt/En1q82ZP3hMlq5SALwC027W5/XbHOm30OTP/ZizdgksDsFkDNFKjhbwQaFPXkzy6XoZXqhW30PzdU93wkmo2kmH6cUPSRYc67o4eDqZTTLZKzxWrgyxAp29GWomkBcGfQxftTHVFkju9FrHsEbX64UuXx1aJw2+qbH/ry+krWNHpQxpxUrGx/Tp3q5XXKtdt035Npyc0EMLj563ya+tj2mW69H9RraIr7gD1A4bGfBg6xYooKCz+Gl8sskBg8BxR22Xh1arJUtN+Tc4dBO7j9w8PFW/ctRc6/mPfgKG6EOTf/vQvwvdJsk/hc6aYjXhU6yQ/eFTuemI3osdDo5GWEsdDJ2+ABjoQ+fnMxoLnQyeAw4hgLfbSUhlorfMzQAAAAASUVORK5CYII=)
Sn![](data:image/png;base64,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)
Sn-1![](data:image/png;base64,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)
Displacement covered in nth sec = Sn – Sn-1
(
)![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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Question 12.A particle covers 10m in first 5s and 10m in next 3s. Assuming constant acceleration. Find initial speed, acceleration and distance covered in next 2s.
Answer:Let the initial speed be u m/s and speed after 5s be v1m/s.
Let acceleration of the particle be a m/s2.
v1 = u + 5a …(using v = u + at) …(1)
Now for first 5s, distance s1![](data:image/png;base64,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)
(2)
For next 3s, v1 will be its initial velocity
and distance s2![](data:image/png;base64,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)
...(3)
Now s1-s2 = 0
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOoAAAAsCAMAAABc+9TVAAAAAXNSR0IArs4c6QAAAJZQTFRFAAAA///b//+22///2/+2tv///9u2/9uQttv/29uQkNv//7Zm27aQ27ZmkLbbZrb/kLaQZrbb25Bm25A6tpA6ZpC2ZpCQOpDbtmY6tmYAkGY6Oma2ZmY6OmaQOmZmkDo6ZjqQAGa2kDoAAGaQZjo6OjqQZjoAOjpmOjoAADqQADpmZgA6ZgAAOgA6OgAAAABmAAA6AAAA/S/5qgAAAAF0Uk5TAEDm2GYAAAKsSURBVHja7VjbdpswEJRQAy5y7Sa0xbKbthDHrlOqsP//cz1CBmGbmwKqIId98JMZaVaj3R0hNMccXePBf7fU8PIA8CL4eRwAIDVCNVtkYZkqg3vkJq93gura1CJBukKYiUWsUo3EVmBtkqqThMWv7aBmqUpkHJ+IfarMrIDleY6CqiTp8SOXBcpAKn2Ev4B9qjjOLhH+eY/c2EgFxluAl89JZJ9pVD7g0Jx2rJclFpHytTKW+iC1PZ0E4gbRECEWGk29Y12/3l8fISxostRHbmyqzy/5znZRYpBFiJC7B4DHhaF7elzN/mK2J12UYs6elPrTp99gaNq46sbPi5bBp6GHDjL8sXRlatoo7/VEmsrkf6Ja2CGTHkSkkl4s4h0XFVSpULHHr7bTmWom0V2bR8AxwBPxOOi0qA7QyoNcdWNaUpI61eA2Kd2p4jgimDUp1N2KviTdCtVi2gqt9CuonghyEihCfajsCe1Dte0yiMUfSZ7QINSvnuvb3n5ZTyXVG+cXpPmXyp7cUK0EhIq42U/ll0suTW6InD9+5VhS/L8Buu1UG6gqD9HvVPFyz6G57lAxYomtUL3htgN0WcARqhGwmqxp37valnrpDOjrHcv+hjfRW6ErVZOXpbCuLCl70otq9nEtVenlJbaTfPslJPbw4xANAF2WqsBvaDbKnnh8R9z9G6mKZLnf66lmq8hbxOCc9yAaAPpCmyfS9B5VsicbSL9+vGqsne/qBmD3Iam7Ue6WA5xNWdFpOlJtgS6vcjiX+UFnsOKJv4/Hj8ziD2Va8yd+M1QHwR/qean/TIvZE7E6M+uM1722EpzfMkzhD3u0hgXGRiHgjrPaqPF1DEc4aXwtazVpfK0aTCaNr1E/8yf+ieJrlIziiX+a+FrTErS2xTHjzzHHiOMfVf9jgRP4kEsAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Putting value of u in equation (2), we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
…(5)
So
(from equation (4))
![](data:image/png;base64,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)
Given, Distance in 8sec = 10m + 10m = 20m
Distance in 10sec![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Distance covered in next 2sec![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGoAAAAsCAMAAAC6/t3UAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAA///b//+22///tv///9u229v//9uQttv/kNv//7Zm27aQ27ZmkLbbZrb/kLaQZrbb25Bm25A6ZpDbOpDbOpC2tmY6tmYAkGY6Oma2OmaQkDo6AGa2kDoAZjo6OjqQZjoAOjpmOjoAADqQADpmZgAAOgAAAABmAAA6AAAAeDaCkQAAAAF0Uk5TAEDm2GYAAAGySURBVHja7Vdhb4IwFHwMGYLaKetWdbDhdJX3///g8kqRzNjSkpItmfehYHL0+tprewL8Z2yy6fpefiI2zwCQSkTExiYVvcpjTM8t4sfcV6lo1gBL5CTFBri53D0qxeoYJ9V55qcUVSU9xDEelsrlWr9Q6TmycVLlcFUPX6V+E1RQ/9MVOdIE0jCHpC5l0PyRlFo2Hyyk9kIqDxJPZleI81ONuIu1VNv6IJUcoKABR29rSCqjA6MKX2JYSD5W6vozpWxhkoG6CfRcK/2B6Jxr7kBLFedZZwsOI6pSZhfcWpUeDjHVfHubHQpaAbWFRZOBbWOmsiQma83n74r2YDqtACB5R8S95bhJa82EpEbcx3DHHX8DOSLbSNyBaqZFKg8ZFHhYQaHOUIEdmiy4FNMHjeUmwhtoj6HrgRmZvRRzSQ1hqrpITT+Bv1HVpG7vbcEnLgqR9Y39glQ3icsKujNNF2yzsiWYUUxTByXo2BSOae3FOYQL37j+E8l2Pw/NNGQ017DgzrQFatdpcWea9yEPzrSl98DMGxGXg1tcdWcaO1DB1iGuujPN/pXqn1NI5h2j8Q1uaDdeLlN1zwAAAABJRU5ErkJggg==)
=![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACkAAAAiCAMAAAD1eQAHAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAA///b//+2/9u2/9uQ29u2kNv//7Zm27aQ27ZmkLbbZrb/Zrbb25Bm25A6ZpDbOpDbtmY6tmYAkGY6Oma2kDo6kDoAZjoAOjpmOjoAADo6ZgA6ZgAAOgA6OgAAAAA6AAAAR+IKJgAAAAF0Uk5TAEDm2GYAAACzSURBVHjazZPBEoIwEENTRCpUatWiKFry/1/pyICoh3bHC+awpzfpNNkFltf6THoAlmRfRMCsq1A+CWsEtvldSlo3vu4TYDkBeYj72peTOrkYqD2gDVRTJDyzG0kaqD3Zb/EX0qSpAz2GES8jtAUs2wo2WvEYbR7cW8j81Bdp0nUsS2rOP3JxS9LM45dK6gv7nQRUzXhLIg23JNHqKNzNA6/iLd4ESRZZVySrmFIKwpQW0QMLQA8WuRsfxQAAAABJRU5ErkJggg==)
= 8.33 m
Question 13.A car starts from rest and travels with uniform acceleration “α” for some time and then with uniform retardation “ β” and comes to rest. The time of motion is “ t”. Find the maximum velocity attained by it.
Answer:Given, initial velocity = 0, acceleration = α and retardation = β
Let the time of accelerated motion be t’ and time of retarded motion be t”, so that t’ + t” = t … (1)
Velocity after time t’, v1 = 0 + αt’ (using v = u + at) …(2)
Now, v1 will be initial velocity for retarded motion and
final velocity = 0 and acceleration![](data:image/png;base64,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)
0 = v1- βt” …(using v = u + at)
Or,
…(3)
Now, in equation (2)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
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![](data:image/png;base64,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)
As, after time t’ , retardation will start so maximum velocity will
be at time t’ which is v1
.
Question 14.A man is 48m behind a bus which is at rest. The bus starts accelerating at the rate of 1 m/s2, at the same time the man starts running with uniform velocity of 10 m/s. What is the minimum time in which the man catches the bus?
Answer:Given, initial velocity of bus, u = 0 and acceleration, a = 1 m/s2.
When man catches the bus, distance between them = 0.
Let at time t sec, man catches the bus first.
Distance covered by man in t sec, d1 = velocity x time
= 10 m/s x t sec
= 10t m
Distance covered by bus in t sec, d2
m
As man was 48m behind, so difference between their distance covered = 48m
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So, Minimum time to catch the bus will be 8sec.
Question 15.A body leaving a certain point “O” moves with a constant acceleration. At the end of the 5th second its velocity is 1.5 m/s. At the end of the sixth second the body stops and then begins to move backwards. Find the distance traversed by the body before it stops.
Determine the velocity with which the body returns to point “O“?
Answer:Given, velocity after 5s = 1.5 m/s
Velocity after 6s = 0 m/s
Let the acceleration be ‘a’ and initial velocity be ‘u’.
For t = 5s,
1.5 = u + 5a …(1) (using v = u + at)
For t = 6s
0 = u + 6a …(2) (using v = u + at)
Subtracting equation (2) from (1), we get
1.5 = -a
Or, a = -1.5 m/s2
Putting value of a in equation (1), we get
u = 9 m/s
So, Distance traversed before stopping = Distance covered in 6s
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Body will again move with same acceleration in opposite direction,
So here initial velocity = 0, acceleration a = -1.5 m/s2 and
displacement s = -27m (direction is opposite)
putting all these values in
we get
-27 =![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Velocity at point “O” = velocity after 6s
= 0 + (-1.5)x6 (using v = u + at)
= -9 m/s
Question 16.Distinguish between speed and velocity.
Answer:![](data:image/png;base64,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)
Question 17.What do you mean by constant acceleration?
Answer:Constant acceleration means change in velocity per unit time should be constant. i.e.,
![](data:image/png;base64,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)
It means body should be changing its velocity with equal amount in equal time interval.
Question 18.When the velocity is constant, can the average velocity over any time interval differ from instantaneous velocity at any instant? If so, give an example; if not explain why.
Answer:No. When the velocity is constant, average velocity over any time interval will not differ from instantaneous velocity at any instant because as velocity is constant, so it will not change during any time interval. It remains same for every point of time. Therefore, average velocity remains equal to the constant velocity.
Question 19.Can the direction of velocity of an object reverse when it’s acceleration is constant? If so give an example; if not, explain why.
Answer:Yes. Direction of velocity of an object can be reversed when it’s acceleration is constant.
For example: When we throw a ball upward, it’s acceleration will be due to gravity i.e. 9.8 m/s2 in downward direction.
After reaching highest point, its direction will be reversed while its acceleration will remain same i.e. due to gravity.
Question 20.A point mass starts moving in a straight line with constant acceleration “a”. At a time t after the beginning of motion, the acceleration changes sign, without change in magnitude. Determine the time t0 from the beginning of the motion in which the point mass returns to the initial position.
Answer:Given, acceleration = a,
initial velocity = 0
time = t
Velocity after time t, v =
…(1)
Now it will become initial velocity.
After acceleration change its sign, let time taken by it to come to rest be t’,
![](data:image/png;base64,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)
…(2)
![](data:image/png;base64,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)
Total time = t + t’
Now distance covered in total time
=![](data:image/png;base64,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)
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=![](data:image/png;base64,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)
=![](data:image/png;base64,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)
=![](data:image/png;base64,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)
=
…(3)
Now after coming to rest it will again start moving in opposite direction. To reach initial point, it has to cover same distance,
So let time taken to cover that distance be t”. Here initial velocity will be 0. Putting value of distance from equation (3), we get.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Time t0![](data:image/png;base64,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)
![](data:image/png;base64,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)
=![](data:image/png;base64,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)
Question 21.Consider a train which can accelerate with an acceleration of 20cm/s2 and slow down with deceleration of 100cm/s2. Find the minimum time for the train to travel between the stations 2.7 km apart.
Answer:Given, total distance need to cover, d = 2.7km = 270000 cm
Let distance covered in accelerated motion be d1 and distance covered in decelerated motion be d2.
So, d1 + d2 = d …(1)
Now for d1, initial velocity will be 0, and acceleration a = 20 cm/s2 and let final velocity be v.
Then, ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFgAAAAuCAMAAACbMC7aAAAAAXNSR0IArs4c6QAAAIpQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OjoAOjpmOmY6OmZmOma2OpDbZgAAZgA6ZjoAZjo6ZjqQZmY6ZpCQZrbbZrb/kDoAkGYAkLbbkNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29uQ29u22/+22////7Zm/9uQ/9u2//+2///bEXkB1gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABh0lEQVRYR+2X3VKDMBCFE9Q2/hXaqhVr0EhVEpL3fz03oUoywwykbMYLzVUvmI/N2bNnKSH/52ND6SqBDHq9J3X2nIAMSHWZCCzyNAXXKSSGUgUi15SULhrF6NkrkcCVj1hamPKiAR5wdUHhoIGJsA5L0TTFcqLXCVxmtZBLLGV9DujL8ZT1yLp4uIP+JTicJpo367VfPhLT58FdJOIABWDFkvgH8hoHrK5fvHoVbK4bHDCR3qZSbEfM0yyNu5jrTk/mLgWHwHzg6VH7iuzYLV3YKYrQuC/u+1fwstPBAzUPSuFXbKogDU+QwmueKS3Mafx2u5kZs4HdRLYn7bZrnpgJDmQyFc1W78yRUcH+WyaBzQEm6jxu500Cc7ojbREVyYYvJqwcbhshYkZVWMdPXDrORqa+Qv9A5iAFOLUxHPcDuY+AiDAYzRnQoPxRDBXcTSvwD1uGui350pnHahyTi6NSCJfgebcuEKVw/2cMz4GZk/YeaanBdY5pCu2rwMWfBR294t954AtNgBvJKgviRwAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
Now for d1, initial velocity will be v, and acceleration a’ = 100 cm/s2 and velocity will be 0.
Then, ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now putting values of d, d1 and d2 in equation (1), we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
And also for d1, let the time taken to travel be t1 then
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
And also for d2, let the time taken to travel be t2 then
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now total time to travel will be t1 + t2![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 22.You may have heard the story of the race between the rabbit and tortoise. They started from same point simultaneously with constant speeds. During the journey, rabbit took rest somewhere along the way for a while. But the tortoise moved steadily with lesser speed and reached the finishing point before rabbit. Rabbit awoke and ran, but rabbit realized that the tortoise had won the race. Draw distance vs time graph for this story.
Answer:![](data:image/png;base64,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)
Question 23.A train of length 50m is moving with a constant speed of 10m/s. Calculate the time taken by the train to cross an electric pole and a bridge of length 250 m.
Answer:Given, speed = 10m/s
Distance needed to be covered to cross electric pole = length of the train
= 50 m
Time taken to cross electric pole![](data:image/png;base64,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)
![](data:image/png;base64,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)
Distance needed to be covered to cross bridge
= length of the train + length of the bridge
= 50 + 250 m
= 300 m
Time taken to cross electric pole![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 24.Two trains, each having a speed of 30km/h, are headed at each other on the same track. A bird flies off one train to another with a constant speed of 60km/h when they are 60km apart till before they crash. Find the distance covered by the bird and how many trips the bird can make from one train to other before they crash?
Answer:Given, speed of each train = 30 km/h and
distance between them = 60km
As they are moving in opposite direction and same speed,
So they will crash at middle of the distance between them, i.e. 30km from each train.
Time taken to travel 30 km by each train =
= 1h
Speed of the bird = 60 km and time = 1h
So distance traveled by bird in 1h = speed × time
= 60 × 1
= 60 km
As trains will come closer to each other, bird can make any number of trips because distance between trains will approach to 0.
So the time taken by bird will also tends to 0. Therefore, bird can make infinite number of trips.
As shown in figure 23, a point traverses the curved path. Draw the displacement vector from given points A to B
Answer:
Displacement is shortest distance between initial point to final point and its direction will be from A to B. So it will be a straight line from point A to point B.
Question 2.
“She moves at a constant speed in a constant direction.”. Rephrase the same sentence in fewer words using concepts related to motion.
Answer:
Sentence can be rephrased as “She moves at constant velocity.” or you can also write it as “She moves at zero acceleration.” as there is no change in its speed or direction resulting in no change in velocity.
Question 3.
What is the average speed of a Cheetah that sprints 100m in 4sec.? What if it sprints 50m in 2sec?
Answer:
Given, distance = 100m and time = 4sec.
Using formula,
If distance = 50m and time = 2 sec, then
= 25 m/s
So speed remains same for both the cases.
Question 4.
Correct your friend who says, “The car rounded the curve at a constant velocity of 70 km/h”.
Answer:
Correct statement will be: “The car rounded the curve at a constant speed of 70 km/h.”
Explanation:
Because velocity denotes speed (magnitude) with direction. And, we know that in circular motion, the direction changes, as shown below:
So velocity will not remain constant but speed will remain constant.
Question 5.
Suppose that the three ball’s shown in figure start simultaneously from the tops of the hills. Which one reaches the bottom first? Explain. See figure 24.
Answer:
First ball will reach the bottom first because all the balls will have same initial speed but path covered by the first ball is the shortest one i.e. straight line between top of the hill and bottom.
So, as distance is shorter and initial speed is same, so first ball will take less time than other two balls.
Question 6.
Distance vs time graphs showing motion of two cars A and B are given. Which car moves fast? See figure 25.
Answer:
Car A moves faster than car B because slope of s-t graph denotes speed.
Here slope of A is greater than slope of B so car A is moving with faster speed than car B.
Question 7.
Draw the distance vs time graph when the speed of a body increases uniformly.
Answer:
Slope of Distance-time graph denotes speed and change in slope of the graph is acceleration. So it must be constant and positive for this graph as speed is increasing.
Question 8.
Draw the distance – time graph when its speed decreases uniformly.
Answer:
Slope of Distance-time graph denotes speed and change in slope of the graph is acceleration. So it must be constant and negative for this graph as speed is decreasing.
Question 9.
A car travels at a velocity of 80 km/h during the first half of its running time and at 40 km/h during the other half. Find the average speed of the car.
Answer:
Let the total running time be t h.
Distance covered in first h
Distance covered in other h
Total distance
So, Average speed
60 km/h
Question 10.
A car covers half the distance at a speed of 50 km/h and the other half at 40km/h. Find the average speed of the car.
Answer:
Let the total distance covered by the car be ‘d’ km.
Time taken to cover first distance, t1
Time taken to cover second distance, t2
Total time = t1 + t2
Therefore, average speed
= 44.44 km/h
Question 11.
Derive the equation for uniform accelerated motion for the displacement covered in its nth second of its motion.
Answer:
Let the total displacement covered after n sec = Sn
Let the initial velocity be u and acceleration be a.
Displacement covered in nth sec = Sn – Sn-1
From the equation of motion, we know that
Sn
Sn-1
Displacement covered in nth sec = Sn – Sn-1
(
)
Question 12.
A particle covers 10m in first 5s and 10m in next 3s. Assuming constant acceleration. Find initial speed, acceleration and distance covered in next 2s.
Answer:
Let the initial speed be u m/s and speed after 5s be v1m/s.
Let acceleration of the particle be a m/s2.
v1 = u + 5a …(using v = u + at) …(1)
Now for first 5s, distance s1
(2)
For next 3s, v1 will be its initial velocity
and distance s2
...(3)
Now s1-s2 = 0
Putting value of u in equation (2), we get
…(5)
So (from equation (4))
Given, Distance in 8sec = 10m + 10m = 20m
Distance in 10sec
Distance covered in next 2sec
=
= 8.33 m
Question 13.
A car starts from rest and travels with uniform acceleration “α” for some time and then with uniform retardation “ β” and comes to rest. The time of motion is “ t”. Find the maximum velocity attained by it.
Answer:
Given, initial velocity = 0, acceleration = α and retardation = β
Let the time of accelerated motion be t’ and time of retarded motion be t”, so that t’ + t” = t … (1)
Velocity after time t’, v1 = 0 + αt’ (using v = u + at) …(2)
Now, v1 will be initial velocity for retarded motion and
final velocity = 0 and acceleration
0 = v1- βt” …(using v = u + at)
Or, …(3)
Now, in equation (2)
As, after time t’ , retardation will start so maximum velocity will
be at time t’ which is v1 .
Question 14.
A man is 48m behind a bus which is at rest. The bus starts accelerating at the rate of 1 m/s2, at the same time the man starts running with uniform velocity of 10 m/s. What is the minimum time in which the man catches the bus?
Answer:
Given, initial velocity of bus, u = 0 and acceleration, a = 1 m/s2.
When man catches the bus, distance between them = 0.
Let at time t sec, man catches the bus first.
Distance covered by man in t sec, d1 = velocity x time
= 10 m/s x t sec
= 10t m
Distance covered by bus in t sec, d2 m
As man was 48m behind, so difference between their distance covered = 48m
So, Minimum time to catch the bus will be 8sec.
Question 15.
A body leaving a certain point “O” moves with a constant acceleration. At the end of the 5th second its velocity is 1.5 m/s. At the end of the sixth second the body stops and then begins to move backwards. Find the distance traversed by the body before it stops.
Determine the velocity with which the body returns to point “O“?
Answer:
Given, velocity after 5s = 1.5 m/s
Velocity after 6s = 0 m/s
Let the acceleration be ‘a’ and initial velocity be ‘u’.
For t = 5s,
1.5 = u + 5a …(1) (using v = u + at)
For t = 6s
0 = u + 6a …(2) (using v = u + at)
Subtracting equation (2) from (1), we get
1.5 = -a
Or, a = -1.5 m/s2
Putting value of a in equation (1), we get
u = 9 m/s
So, Distance traversed before stopping = Distance covered in 6s
Body will again move with same acceleration in opposite direction,
So here initial velocity = 0, acceleration a = -1.5 m/s2 and
displacement s = -27m (direction is opposite)
putting all these values in we get
-27 =
Velocity at point “O” = velocity after 6s
= 0 + (-1.5)x6 (using v = u + at)
= -9 m/s
Question 16.
Distinguish between speed and velocity.
Answer:
Question 17.
What do you mean by constant acceleration?
Answer:
Constant acceleration means change in velocity per unit time should be constant. i.e.,
It means body should be changing its velocity with equal amount in equal time interval.
Question 18.
When the velocity is constant, can the average velocity over any time interval differ from instantaneous velocity at any instant? If so, give an example; if not explain why.
Answer:
No. When the velocity is constant, average velocity over any time interval will not differ from instantaneous velocity at any instant because as velocity is constant, so it will not change during any time interval. It remains same for every point of time. Therefore, average velocity remains equal to the constant velocity.
Question 19.
Can the direction of velocity of an object reverse when it’s acceleration is constant? If so give an example; if not, explain why.
Answer:
Yes. Direction of velocity of an object can be reversed when it’s acceleration is constant.
For example: When we throw a ball upward, it’s acceleration will be due to gravity i.e. 9.8 m/s2 in downward direction.
After reaching highest point, its direction will be reversed while its acceleration will remain same i.e. due to gravity.
Question 20.
A point mass starts moving in a straight line with constant acceleration “a”. At a time t after the beginning of motion, the acceleration changes sign, without change in magnitude. Determine the time t0 from the beginning of the motion in which the point mass returns to the initial position.
Answer:
Given, acceleration = a,
initial velocity = 0
time = t
Velocity after time t, v = …(1)
Now it will become initial velocity.
After acceleration change its sign, let time taken by it to come to rest be t’,
…(2)
Total time = t + t’
Now distance covered in total time
=
=
=
=
=
=…(3)
Now after coming to rest it will again start moving in opposite direction. To reach initial point, it has to cover same distance,
So let time taken to cover that distance be t”. Here initial velocity will be 0. Putting value of distance from equation (3), we get.
Time t0
=
Question 21.
Consider a train which can accelerate with an acceleration of 20cm/s2 and slow down with deceleration of 100cm/s2. Find the minimum time for the train to travel between the stations 2.7 km apart.
Answer:
Given, total distance need to cover, d = 2.7km = 270000 cm
Let distance covered in accelerated motion be d1 and distance covered in decelerated motion be d2.
So, d1 + d2 = d …(1)
Now for d1, initial velocity will be 0, and acceleration a = 20 cm/s2 and let final velocity be v.
Then,
Now for d1, initial velocity will be v, and acceleration a’ = 100 cm/s2 and velocity will be 0.
Then,
Now putting values of d, d1 and d2 in equation (1), we get
And also for d1, let the time taken to travel be t1 then
And also for d2, let the time taken to travel be t2 then
Now total time to travel will be t1 + t2
Question 22.
You may have heard the story of the race between the rabbit and tortoise. They started from same point simultaneously with constant speeds. During the journey, rabbit took rest somewhere along the way for a while. But the tortoise moved steadily with lesser speed and reached the finishing point before rabbit. Rabbit awoke and ran, but rabbit realized that the tortoise had won the race. Draw distance vs time graph for this story.
Answer:
Question 23.
A train of length 50m is moving with a constant speed of 10m/s. Calculate the time taken by the train to cross an electric pole and a bridge of length 250 m.
Answer:
Given, speed = 10m/s
Distance needed to be covered to cross electric pole = length of the train
= 50 m
Time taken to cross electric pole
Distance needed to be covered to cross bridge
= length of the train + length of the bridge
= 50 + 250 m
= 300 m
Time taken to cross electric pole
Question 24.
Two trains, each having a speed of 30km/h, are headed at each other on the same track. A bird flies off one train to another with a constant speed of 60km/h when they are 60km apart till before they crash. Find the distance covered by the bird and how many trips the bird can make from one train to other before they crash?
Answer:
Given, speed of each train = 30 km/h and
distance between them = 60km
As they are moving in opposite direction and same speed,
So they will crash at middle of the distance between them, i.e. 30km from each train.
Time taken to travel 30 km by each train == 1h
Speed of the bird = 60 km and time = 1h
So distance traveled by bird in 1h = speed × time
= 60 × 1
= 60 km
As trains will come closer to each other, bird can make any number of trips because distance between trains will approach to 0.
So the time taken by bird will also tends to 0. Therefore, bird can make infinite number of trips.