Question

A driver of a car in motion sees a deer on the road. The driver hits the brakes which provide an acceleration of -7.0 m/sec^2. If the car’s initial velocity was 25 m/sec, how far will the car travel before coming to a stop?

Answer 1

Under constant acceleration, we have

`v^2-{v_0}^2 = 2ax`

where
`v` is final velocity,
`v_0` is initial velocity,
`a` is acceleration, and
`x` is distance.

Solving for
`x` gives

`x = \frac{v^2-{v_0}^2}{2a}`

Then if the car starts with speed 25 m/s and acceleration -7.0 m/s², and comes to a rest (so that
`v=0`), we have

`x = (-\left(25(\rm m)/(\rm s)\right)^2)/(2\left(-7.0(\rm m)/(\mathrm s^2)\right)) \approx \boxed{45\,\mathrm m}`