Question

At an accident scene on a level road, investigators measure a car's skid mark to be 88 m long. It was a rainy day and the coefficient of friction was estimated to be 0.42. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes. (Why does the car/s mass not matter?)

Answer 1

Answer:

The speed was 26.91m/s (96.9 km/h)

Explanation:

Here you have to consider that at the beginning you have an amount of kinetic energy (K) that is dissipated because of the work done by friction forces (T). Since the car is stopped after the accident, all the energy has been dissipated. Thus, $K=T$.

The definition of the kinetic energy is $K=1/2*m*v^2$.

The work done by the friction forces is: $T=f*(m*g)*d$. Where f is the friction coefficient, g is the gravity acceleration, m is the mass of the car and d is the skid marks longitude. Therefore,

$1.2*m*v^2=f*(m*g)*d$

Since m is in both sides it can be cancelled so it is not necessary to considered.

Then, the speed is determined by the following equation:

$v=\sqrt{2*f*g*d} =\sqrt{2*0.42*9.8m/s^2*88 m}=26.91 m/s$