A driver loses control of his car and the car slams into a bumper protecting a b

Question

A driver loses control of his car and the car slams into a bumper protecting a bridge, compresses the bumper, and bounces back out. The driver steps on his brakes just as the car hits the bumper, so that the tires skid for the entire time of the collision. (The friction will be in a direction opposite to the velocity.) The police want to use the distance travelled, as measured by the skid marks on the road, to determine the initial speed of the car. The mass of the car is 925 kg, the spring constant of the bumper is 225000 N/m, and the frictional force of the tires on the road is 8500 N. If the skid marks show that the bumper compressed a maximum distance of 1.0 m, what was the initial velocity of the car? Give your answer in m/s to three digits. Do not include units in your answer.

Explanation / Answer

since the tires are skidding, there are 2 forces that stop the car,spring force from the bumper and the friction.
Fsp=225000x1=225000N

Ffriction=8500
total force=233500N
deceleration=233500/mass=233500/925=252.43 m/s^2

now v2=u2+2as

v=0 , a= -252.43 , s=1m

u2=2x252.43x1

u=22.47m/s

initial velocity=22.5

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