A body is initially at rest. It undergoes one-dimensional motion … - Vidyadip

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 :
(a) $t^{1 / 2}$
(b) $t$
(c) $t^{3 / 2}$
(d) $t^2$.

✓

Answer

Let mass of body = m
Constant acceleration of body = a
Initial velocity u = 0
Velocity at time t = v
From first equation of motion
$
\begin{array}{l}
v=u+a t \\
v=0+a t=a t
\end{array}
$
Force $F =m a$ (constant)
$
\begin{aligned}
\therefore \quad \text { Power } P & =\text { F.v. } \\
& =m a \cdot a t=m a^2 t \\
P & \propto t
\end{aligned}
$
Hence, correct answer is (b).

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