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**1. The problem and given data**

You are a police officer and your squad car is at rest on the

shoulder of an interstate highway when you notice a car passing you at

its top speed of

**85 mi/h**. You jump in your car, start the engine,

and find a break in the traffic, a process which takes

**25 s**. You

know from the squad car's manual that when it starts from rest

with its accelerator pressed to the floor, the magnitude of its

acceleration is

**a=a'-bt^2**; (where

**a'=2.5m/s^2 and b=0.0028m/s^4)**until

**a'=bt^2**and then remains zero thereafter.

Can you catch the car before it reaches the next exit

**5.3 mi**away?

**2. Any relevant equations**

a=a'-bt^2, where a'=2.5m/s^2 and b=0.0028m/s^4

**3. The attempt**

I'm having trouble using the correct values. I took the integral of acceleration, to obtain velocity, then I took the integral of velocity to obtain distance.

My reasoning is that if I can find the distance, I can find out the exact value before or after 5.3 mi.

My equation ultimately is: x=(a't^2)/2 - (bt^4)/12 + v't +x'

where a', t and b are given. I used 85 mi/hr for v' and x' =0. I get the wrong answer.

The right answer is

**3.8mi**.

Any advice/suggestions will be greatly appreciated for this struggling physics student

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