Question

At an accident scene on a level road, investigators measure a car's skid mark to be 84 m long. It was a rainy day and the coefficient of friction was estimated to be 0.36.

Answer 1

The given data is incomplete. The complete question is as follows.

At an accident scene on a level road, investigators measure a car's skid mark to be 84 m long. It was a rainy day and the coefficient of friction was estimated to be 0.36.  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?)

Explanation:

Let us assume that v is the final velocity and u is the initial velocity of the car. Let s be the skid marks and $\mu$ be the friction coefficient and m be the mass of car.

Hence, the given data is as follows.

                v = 0,     s = 84 m,     $\mu$ = 0.36

According to Newton's law of second motion the expression for acceleration is as follows.

                      F = ma

                 $-\mu N$ = ma

                 $-\mu mg$ = ma

                      a = $-\mu g$

Also,    

               $v^{2} = u^{2} + 2as$

              $(0)^{2} = u^{2} + 2(-\mu g)s$

                  $u^{2} = 2(\mu g)s$

                            = $\sqrt{2(0.36)(9.81 m/s^{2})(84 m)}$

                            = 24.36 m/s

Thus, we can conclude that the speed of the car when the driver slammed on (and locked) the brakes is 24.36 m/s.