Question

At an accident scene on a level road, investigators measure a car’s skid mark to be 95 m long. It was a rainy day and the coefficient of friction was estimated to be 0.45. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes. Answer: _________ m/s (round to the nearest tenth)

Answer 1

When an object decelerates to a stop from an initial speed v with an acceleration a, the distance d traveled by the object is given by:

$d=\frac{v^2}{2a}$

Then, the initial speed can be calculated as:

$v=\sqrt{2ad}$

On the other hand, the acceleration of an object skidding through a horizontal surface with a coefficient of friction μ is:

$a=\mu g$

Where g=9.81m/s^2 is the gravitational acceleration.

Then, the initial speed is given in terms of known variables as:

$v=\sqrt{2\mu gd}$

Replace the values to find the initial speed of the car:

$v=\sqrt{2(0.45)(9.81\frac{m}{s^2})(95m)}=28.9...\frac{m}{s}$

Therefore, the initial speed of the car was 28.9m/s.