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Energy is the conserved quantity associated to time-translation invariance and represents the work a system is capable of doing. Use this tag for questions about energy, and consider adding the [energy-conservation] tag if it is specifically about its conservation.
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Why ball thrown with higher velocity hurts more?
Your line of thinking is correct regarding your first point. And yes time of contact would be necessary in calculating the force.
You must have noticed that while catching a ball if you retract your …