First slide

Power

Question

A body of mass M is accelerated uniformly from rest to a speed V in time T. The instantaneous power delivered to the body as a function of time is given by

Moderate

A

$\frac{1}{2} \frac{M V^{2}}{T^{2}} \cdot t$
B

$\frac{1}{2} \frac{M V^{2}}{T^{2}} \cdot t^{2}$
C

$\frac{M V^{2}}{T^{2}} \cdot t$
D

$\frac{M V^{2}}{T^{2}} \cdot t^{2}$

Solution

$Power = force . velocity h e r e f o r c e = M a; a c c e l e r a t i o n a = \frac{v e l o c i t y}{t i m e} \Rightarrow v = a t; s u b s t i t u t e P = M a . a t P = M a^{2} t s u b s t i t u t e g i v e n v a l u e s o f a c c e l e r a t i o n = \frac{V}{T} P = M {(\frac{V}{T})}^{2} t P = M {\frac{V}{T^{2}}}^{2} t$

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