Question

You are arguing over a cell phone while trailing an unmarked police car by 25m. Both you and the police car are traveling at 100 km/hr. Your argument diverts your attention from the police car for 2.0s. At the beginning of the 2.0s, the police officer begins braking suddenly at 5.0 m/s2.
What is the separation between the two cars when your attention finally returns?
Suppose that you take another 0.40s to realize your danger and begin braking. If you too brake at 5.0 m/s2, what is your speed when you hit the police car?

Answer 1

I converted 100km/hr to 27.78 m/s and ended up finding 20 as the separation distance, but I can't seem to figure out the secon question, being the speed when you hit the police car.

Answer 2

in effect - for the first part the police car is accelerating towards you @ 5m/s^s

s=ut + 0.5 at^2
s= 0 + 0.5*5*4

This is the distance the police gets closer by in the 2 s. You start off 25m apart so you have to subtract the value above from 25.

I don't think 20 is the correct answer.

For the second you need to work out the speed of the police car when you hit the brakes.

Since you decelerate at the same rate as the police car your relative velocity remains the same.

You know how far apart you are - you know your relative speed so oyu can work out how long it takes to collide.

Then work out your speed from v=u +at

Answer 3

sorry - I didn't take into account the extra 0.4 s

this just adds to the 2s that oyu weren't paying attention

so s=0 + 0.5 * 5 * 2.4^2

The rest still holds