Acar traveling at 20.0 m/s (about 45 mph) slams on its brakes to avoid hitting a biker and decelerates at 7.00 m/s2 . how far does the car travel assuming that the driver’s reaction time is 1.5s?

To solve for the distance covered.

a) Solve for distance before applying the brake which is during the reaction time.

reaction time = 1.5 seconds, and the speed is 20m/s.

Distance = 20m/s * 1.5s = 30 m.

b) Distance covered during deceleration.

v² = u² + 2as

Deceleration, a = -7 m/s²

We would assume it decelerates to a stop.  v = 0, u = 20 m/s

v² = u² + 2as

0² = 20² + 2*(-7)s

0 = 20*20 - 14s

0 = 400 - 14s

14s = 400

s = 400/14

s ≈ 28.57 m

Hence distance covered = distance covered during reaction time + distance covered during deceleration

                                       = 30 m + 28.57 m = 58.57 m

So the car traveled ≈ 58.57 m 

Hope this explains it.

The solution to the system of equations (-2,2)