The brakes of a car moving at 14m/s are applied, and the car comes to a stop in 4s. (a) what was the cars acceleration? (b) how long would the car take to come to a stop starting from 20m/s with the same acceleration? (c) how long would the car take to slow down from 20m/s to 10m/s with the same acceleration?

(a)

The car's acceleration is given by

where

v = 0 is the final velocity

u = 14 m/s is the initial velocity

t = 4 s is the time elapsed

Substituting,

where the negative sign means the car is slowing down.

(b) 5.7 s

We can use again the same equation

where in this case we have

is again the acceleration of the car

v = 0 is the final velocity

u = 20 m/s is the initial velocity

Re-arranging the equation and solving for t, we find the time the car takes to come to a stop:

(c)

As before, we can use the equation

Here we have

is again the acceleration of the car

v = 10 is the final velocity

u = 20 m/s is the initial velocity

Re-arranging the equation and solving for t, we find

+15-35=-20

going in opposite directions