A body is initially at rest. It undergoes one-dimensional motion with
Question.
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) $t$

(iii) $t^{\frac{3}{2}}$

(iv) $t^{2}$

solution:

Answer: (ii) t

Mass of the body = m

Acceleration of the body = a

Using Newton’s second law of motion, the force experienced by the body is given by the equation:

F = ma

Both m and a are constants. Hence, force F will also be a constant.

F = ma = Constant … (i)

For velocity v, acceleration is given as,

$a=\frac{d v}{d t}=$ Constant

$d v=$ Constant $\times d t$

$v=\alpha t$ $\ldots(i i)$

Where, $\alpha$ is another constant

$v \propto t$ $\ldots$ (iii)

Power is given by the relation:

P = F.v

Using equations (i) and (iii), we have:

$P \propto t$

Hence, power is directly proportional to time.
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