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

$x = \dfrac{v^2-{v_0}^2}{2a}$

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

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