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 âµk = 0.550 for your tires on the road, find the speed of your car as it collides with the other car?

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)

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