# Help with a police car distance physics problem

## Homework Statement

You are arguing over a cell phone while trailing an unmarked police car by 26.0 m; both your car and the police car are traveling at 110 km/h. Your argument diverts your attention from the police car for 2.0 s (long enough for you to look at the phone and yell,“I won't do that!”). At the beginning of that 2.0 s, the police officer begins braking suddenly at 6.00 m/s2. (a) What is the separation between the two cars when your attention finally returns? Suppose that you take another 0.400 s to realize your danger and begin braking. (b) If you too brake at 6.00 m/s2, what is your speed (in km/h) when you hit the police car?

## The Attempt at a Solution

110000m/h = 30.55meters sec

distance between = 26 - 1/2 (6) t^2
at 2 seconds distance = 26 -0.5(6) 2^2
= 14 meters

distance when you begin braking
distance = 26 -0.5(6) 2.4^2
= 9 meters
police car speed when you begin braking
v= 30.55 -6 (2.4)
=16.55m/s
distance during braking
d = 9 - (30.55-16.55)t - 0.5 (6-6)t^2
time to impact
0 = 9- 14t
t= 9/14 sec= .642 sec past the 2.4 seconds

police car speed at 2.4 + .624 sec

v= 30.55 - ( 3.024 )6
v= 12.40 m/s

= 26.8 m/s

**this is my thought on the problem. I got part a correct with 14 m but I seem to have gone wrong after that and am not sure what I did wrong