The hypothesis; greater fraction of kinetic energy is lost from the system during the collision when the speed of the first cart is greater is; Correct
In an Inelastic Collision, energy is not conserved . Now, the loss of energy could be in the form of friction, vibrational energy, sound, heat energy, e.tc.
Now, for example frictional energy is proportional to the velocity. The, the greater the velocity, the greater the loss of energy. This is also true about vibrational energy, sound, heat energy, e.tc.
Thus, we can conclude that the hypothesis is correct.
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