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Physics 1 2nd edition Q 5.39 CARTS

Question

Everyone in my household has tried working this problem and cannot come up with the given answer.

A force F acts on a cart in motion on a frictionless surface to change its velocity.  The initial velocity of the cart and final velocity of each cart are shown.  You do not know how far or in which direction the cart traveled.  Rank the energy required to change each cart's velocity from greatest to least.

Cart A changes from 5 m/s to 2 m/s and has a mass of 2 kg.

Cart B changes from 3 m/s to -3 m/s and has a mass of 3 kg.

Cart C changes from 5 m/s to 6 m/s and has a mass of 5 kg.

Cart D changes from -1 to 2 m/s and has a mass of 4 kg.

Does this problem use W = 1/2 mv^2 formula?  Does mass matter since it's frictionless and is moving in the x direction?

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