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A car moving at 50 km/h skids 15 m with locked brakes.How far will the car skid with locked brakes at 150km/h

[العباس]

Work done by the brakes changes the car's KE from its initial value to zero. This work is equal to the force of friction causing the skid marks multiplied by the length of the skid marks since
work = force x distance
When the car's speed is increased from 50 km/h to 150 km/h, its KE is increased by nine times! Remember that KE is given by

KE = (1/2) m v2
so increasing v by three means that KE increases by nine. The force of friction between the road and the skidding tires does not change appreciably so the distance or length over which the force is applied must increase nine times as well. That means we would expect skid marks to be about 9 x 15 m or 135 m long.