Question

In coming to a stop, a motorcycle leaves skid marks 100m long on the highway. Assume that the motorcycle slows down at a constant rate of -7.5m/s², estimate the speed of the car just before breaking.

Answer 1

We can find the speed of the motorcycle just before breaking from the kinematic equation:

$$v^2=v_0^2+2as,$$

here, $v=0\ \dfrac{m}{s}$ is the final velocity of the motorcycle, $v_0$ is the initial velocity of the motorcycle (just before breaking), $a=-7.5\ \dfrac{m}{s^2}$ is the deceleration of the motorcycle and $s=100 \ m$ is the distance traveled by the motorcycle when it is breaking.

From this formula we can calculate the speed of the motorcycle just before breaking:

$$v_0=\sqrt{-2as}=\sqrt{-2\cdot(-7.5\ \dfrac{m}{s^2})\cdot 100\ m}=38.73\ \dfrac{m}{s}.$$

Answer:

$v_0=38.73\ \dfrac{m}{s}.$