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If a freely falling body starts from rest, then its displacement is given by $ s = \frac{1}{2} gt^2 $. Let the velocity after a time $ T $ be $ v_T $. Show that if we compute the average of the velocities with respect to $ t $ we get $ v_{ave} = \frac{1}{2} v_T $, but if we compute the average of the velocities with respect to s we get $ v_{ave} = \frac{2}{3} v_T $.

$\frac{2}{3} v_{T}$

Applications of Integration

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