Problem

(II) Police investigators, examining the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.

Solution 70GP: The coefficient of kinetic friction come into play when the object is set into motion, that is there is relative motion between between the two surface, and we have calculate initial speed of the car. Step 1 of 3 Concept: Newton’s second law: The force F acts on mass m produces an acceleration a in the object. Mathematically, F=ma. Frictional force also acts on the surface of the bodies in contact whenever their is relative motion between between the two bodies. Step 2 of 3 Length of the skid marks s = 72 m Coefficient of kinetic friction k = 0.80 Final velocity of the car v = 0 m/s Initial velocity of the car u = On the level road, the frictional force is the only force which is responsible for slowing the automobile. If frictional force of magnitude F , acts on the car causing the deceleration of a m/s acting on fr the car of mass m kg, using Newton's Second Law we get, F fr= ma k N = ma kg = ma a = gk a = 0.80×9.8 2 a = 7.84 m/s 2 Thus the car was decelerating with a = 7.84 m/s .