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Understanding derivation of kinetic energy from impulse?
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Doc Al
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May24-09, 07:00 AM
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While
impulse
is ∫Fdt,
work
is ∫Fdx. Since force can be viewed as the rate of change of momentum, you have F = dp/dt = m dv/dt. Thus:
W = ∫Fdx = ∫m (dv/dt) * dx = m∫dv*(dx/dt) = m∫v dv = ½mv² (which is kinetic energy).
Make sense?