First slide

Power

Question

A ball of mass m accelerates uniformly from rest to v₁ in time t₁ • As a function of t, the instantaneous power
delivered to the body is

Moderate

A

$\frac{m v_{1} t}{t_{1}}$
B

$\frac{m {v^{2}}_{1} t^{2}}{t_{1}}$
C

$\frac{m v_{1} t^{2}}{t_{1}}$
D

$\frac{m v_{1}^{2} t}{t_{1}^{2}}$

Solution

$From v = u + a t, v_{1} = 0 + a t_{1}$
$F = m a = \frac{m v_{1}}{t_{1}}$ $(∵ a = \frac{v_{1}}{t_{1}})$
Velocity acquired in t second $= a t \Rightarrow v = \frac{v_{1}}{t_{1}} t$
Power $= F v = (\frac{m v_{1}}{t_{1}}) (\frac{v_{1}}{t_{1}} t) = (\frac{m v_{1}^{2}}{t_{1}^{2}}) t$

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