Answer
The motorcycle travels a distance of $~~90~meters~~$ during the braking period.
Work Step by Step
We can find the acceleration:
$v_f = v_0+at$
$a = \frac{v_f-v_0}{t}$
$a = \frac{15~m/s-30~m/s}{3.0~s}$
$a = -5.0~m/s^2$
We can find the distance the motorcycle travels during the braking period until the motorcycle comes to a stop:
$v^2 = v_0^2+2ax$
$x = \frac{v^2-v_0^2}{2a}$
$x = \frac{0-(30~m/s)^2}{(2)(-5.0~m/s^2)}$
$x = 90~m$
The motorcycle travels a distance of $~~90~meters~~$ during the braking period.
