At an accident scene on a level road, investigators measure a car's skid mark (mass of car is M) to be of length d. It was a rainy day and the coefficient of friction was estimated to be μk.

A) Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes. B) Why does the car's mass not matter?1) Since both the change in kinetic energy and the work done by friction are proportional to the mass. The mass cancels out of the equation. 2) Since the work done by friction does not depend on mass. 3) Since the change in kinetic energy and the work done by friction do not depend on mass.

1) Since both the change in kinetic energy and the work done by friction are proportional to the mass. The mass cancels out of the equation

Explanation:

The kinetic friction works against the kinetic energy of the car and the car stops when these two equalises.

friction force = μk x R, μk is coefficient of kinetic friction and R is reaction from the ground.

= μk x mg

work done by friction

= force x displacement

= μk x mg x d

kinetic energy of car at the time of accident = 1/2 m v²

kinetic energy = work done by friction

1/2 m v² = μk x mg x d

d = v² / (2 μk x g)

v² = 2dμk g

v = √ (2dμk g)

Since both the change in kinetic energy and the work done by friction are proportional to the mass. The mass cancels out of the equation