It takes four times the work and four times the stopping distance.
Given:
original speed of car = x
brakes applied so final speed = 0
moving speed of another car = 2x
To Find:
work done to stop the car
Solution: Work is done whenever a force moves something over a distance. You can calculate the energy transferred, or work done, by multiplying the force by the distance moved in the direction of the force.
Work done is given by
W = KE(final) - KE(initial)
W = 1/2m(v)^2 - 1/2m(u)^2
W = 1/2m(0 - (x)^2)
W = 1/2m(4x^2)
W = 4(1/2mx^2)
W = 4W
So, work done will be 4 times initial work
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