Question

While driving your car on a level road at 60.0 mph, the traffic ahead of you comes to a sudden stop. you apply your brakes in a panic, causing them to lock. your car skids for 57.0 m before hitting the car in front of you. if µk = 0.550 for your tires on the road, find the speed of your car as it collides with the other car?

Answer 1

First let us calculate the acceleration of the car.

The net force is equivalent to the frictional force:

m a = µk m g

a = µk g

a = 0.550 * 9.8 m/s^2

a = 5.39 m/s^2 (negative direction) = -5.39 m/s^2

Then we use the equation:

v^2 = vi^2 + 2 a d

where v is final speed or velocity, vi is initial speed = 60 mph = 26.8224 m/s, d is distance

v^2 = (26.8224 m/s)^2 + 2 (-5.39 m/s^2) * 57 m

v^2 = 104.98 m^2/s^2

v = 10.25 m/s (ANSWER)