When a driver presses the brake pedal, his car stops with an acceleration of - 0.5 m/s². How far will the car travel while coming to a complete stop if its initial speed was 8 m/s?

64 m

Explanation:

Using the following symbols

x: distance

v: velocity

a: constant acceleration

t: time

v₀: initial velocity

x₀: initial position

The equations of motion for a constant acceleration are given by:

(1) x = 0.5at²+v₀t+x₀

(2) v = at+v₀

From equation (2) you can calculate the time t it takes the car to come to a complete stop.

(3) t = (v-v₀) / a

Now you plug equation (3) in equation (1):

(4) x = 0.5a ((v-v₀) / a) ²+v₀ ((v-v₀) / a) + x₀

In equation (4) the position x is the only unknown.