Question

A car 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?

Answer 1

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.