A body of mass m, accelerates uniformly from rest to $\mathrm{v}_{1}$ in time $\mathrm{t}_{1}$. The instantaneous power delivered to the body as a function of time $t$ is

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

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

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

JEE Main · 2004 · 24 Apr 2004 · Offline · Work, Power & Energy

A body of mass m, accelerates uniformly from rest to

v_{1}

in time

t_{1}

. The instantaneous power delivered to the body as a function of time

t

(A) $\frac{m v _{1} t}{t _{1}}$
(B) $\frac{m v _{1}^{2} t}{t _{1}^{2}}$ ✓ Correct
(C) $\frac{m v _{1} t ^{2}}{t _{1}}$
(D) $\frac{m v _{1}^{2} t}{t _{1}}$

Answer: (B)

Solution

The power delivered is

P = F \cdot v = ma v

. Starting from rest with uniform acceleration,

a = \frac{v _{1}}{t _{1}}

, and at time

t

the speed is

v = a t = \frac{v _{1}}{t _{1}} t

. Substituting,

P = m \cdot \frac{v _{1}}{t _{1}} \cdot \frac{v _{1} t}{t _{1}} = \frac{m v _{1}^{2} t}{t _{1}^{2}}

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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