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A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time $t$ is proportional to(i) $t^{\frac{1}{2}}$(ii) $t^{\frac{3}{2}}$(iii) $t^{2}$(iv) $t$
A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time $t$ is proportional to
(i) $t^{\frac{1}{2}}$
(ii) $t^{\frac{3}{2}}$
(iii) $t^{2}$
(iv) $t$
CBSE | Class 11 | NCERT | Physics | Work, Energy, and Power
A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time $t$ is proportional to
(i) $t^{\frac{1}{2}}$
(ii) $t^{\frac{3}{2}}$
(iii) $t^{2}$
(iv) $t$

Let the body mass be $m$

Let the Acceleration be $a$

According to Newton’s second law of motion, we have,

$F=m a($ constant $)$

As, $\mathrm{a}=\frac{d v}{d t}=$ constant

$d v=d t \times$ constant

On integrating we get,

Where, $\alpha$ is a constant

$\mathrm{v} \propto \mathrm{t} \rightarrow 2$

The relation of power is given by:

From equation $1 \& 2$

$P \propto t$

Thus, we can say that power is proportional to time.

i

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