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If twice the force is exerted over twice the distance how

When an average force F is exerted over a certain distance on a shopping cart of mass m, its kinetic energy increases by 12 mv2.

(a) Use the work-energy theorem to show that the distance over which the force acts is mv2/2F.

Am I on the right track? UGH so very frustrated!

Kinetic energy = 1/2 mass x speed2

KE = 1/2 mv2

F average = delta MV (mass x velocity)

Work done = F1= F v2m / 2F = mv2/2F

(b) If twice the force is exerted over twice the distance, how does the resulting increase in kinetic energy compare with the original increase in kinetic energy?

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Physics: If twice the force is exerted over twice the distance how

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