Ncert Exercises & Solutions

A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in the figure correctly shown the displacement-time curve for its motion?

1.		2.
3.		4.

(b) Hint: Use dimensional analysis to find the relation between the distance and time.

Step 1: Use formula of power.

Given, power = constant
We know that power (P)

$P = \frac{dW}{dt} = \frac{F . ds}{dt} = \frac{Fds}{dt} (∵ body is moving unidirectionally)$

Hence, F.ds = Fds cos 0 $°$

$P = \frac{Fds}{dt} = constant (∵ P = constant by question)$

Step 2: Use dimensional analysis.

Now, writing dimensions

$[F] [v] = constant$
$\Rightarrow [{MLT}^{- 2}] [{LT}^{- 1}] = constant$
$\Rightarrow L^{2} T^{- 3} = constant (∵ mass is constant)$
$\Rightarrow L \propto T^{3 / 2} \Rightarrow Displacement (d) \propto t^{3 / 2}$

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