A body of mass $m$ accelerates uniformly from rest to $v_{1}$ in time $t_{1}$ . As a function of time $t$ , the instantaneous power delivered to the body is [2004 AIEEE]

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

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

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

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

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Solution

The correct option is D
$\frac{m v_{1}^{2} t}{t_{1}^{2}}$

$P = \to F . \to v = m a \times a t = m a^{2} t$ [ as u = 0 ]

$= m (\frac{v_{1}}{t_{1}})^{2} t = \frac{m v_{1}^{2} t}{t_{1}^{2}}$ [ As a = $\frac{v_{1}}{t_{1}}$ ]

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A body of mass $m$ accelerates uniformly from rest to $v_{1}$ in time $t_{1}$ . As a function of time $t$ , the instantaneous power delivered to the body is [2004 AIEEE]

The correct option is D
$\frac{m v_{1}^{2} t}{t_{1}^{2}}$

$P = \to F . \to v = m a \times a t = m a^{2} t$ [ as u = 0 ]

$= m (\frac{v_{1}}{t_{1}})^{2} t = \frac{m v_{1}^{2} t}{t_{1}^{2}}$ [ As a = $\frac{v_{1}}{t_{1}}$ ]