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In the following diagram, a force F acts on a cart in motion on a frictionless surface. The initial and final velocities of each cart are shown. Rank the energy required to change each cart's velocity from greatest to least.

A: Weighs 2 kg, 5 m/s to 2 m/s - Change in KE = 1/2*2*(2*2-5*5) J = -21 J

B: Weighs 3 kg, 3 m/s to -3 m/s - Change in KE = 1/2*3*(3*3-(-3)*(-3)) J = 0 J

C: Weighs 5 kg, 5 m/s to 6 m/s - Change in KE = 1/2*5*(6*6-5*5) J = 27.5 J

D: Weighs 4 kg, -1 m/s to 2 m/s - Change in KE = 1/2*4*(2*2-(-1)*(-1)) J = 6 J

The answer says that the ranking is C, B, A, D, which doesn't make any sense to me given the calculations I made. Can someone please explain what I did wrong, or clarify the question?

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From the AP Physics 1 Essentials book...  a tricky question.

 

For B, because you're passing through the zero point, you find the energy going from 3 m/s to 0 m/s, and then the energy going from 0 m/s to -3 m/s, and add them.  Same idea with D.  It requires you to think past the standard definition and understand what sort of work must be done to accomplish the feat.

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