physics
posted by jeremy steadman .
A car moving at 50 km/h skids 15 m with locked brakes. Show that a car moving at 150 km/h will skid 135 m with locked brakes. (Hint: The force doing work during the skidding is the same for both speeds. Use the work–energy theorem.)

work = force * distance
= F d
F the same for both
work done = kinetic energy lost
= .5 m v^2
same m
V2 = 3 V1
so
V2^2 = 9 V1^2
so work done at 50 = (1/2)m V1^2 = F d1
and at 150 = (1/2) m (9 V1 ^2) = F d2
so
d2/d1 = 9
9 * 15 = 135