You slam on the brakes of your car in a panic and skid a distance X on a straight, level road.

If you had been traveling half as fast under the same road conditions, you would have skidded a distance:
a) X/4.00.
b)X/8.00.
c)2.00X.
d)X/2√.

Please explain the answer.

Question

You slam on the brakes of your car in a panic and skid a distance X on a straight, level road. 

If you had been traveling half as fast under the same road conditions, you would have skidded a distance:
a) X/4.00.
b)X/8.00.
c)2.00X.
d)X/2√.

Please explain the answer.

anonymous · Answer

F = Friction force = (coefficient) (weight) and will be constant

Work due to friction = (F)(distance) = change in kinetic energy

F X = (1/2) m v^2

X is proportional to square of the velocity,

so cut velocity in half and distance is cut to X/sqrt(2)