# HELP with Police + Speeding Car :velocity, acceleration, displacement

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.

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