Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Formula used: $P=\frac{W}{t}=\frac{\overrightarrow{F}.\overrightarrow{d}}{t}=\overrightarrow{F}.\overrightarrow{v}$

Given,

Power from a constant power source

$P=\frac{W}{t}=\frac{\overrightarrow{F}.\overrightarrow{d}}{t}=\overrightarrow{F}.\overrightarrow{v}=Constant$

Now, by dimensional analysis

$\left[F\right]\left[v\right]=constant$

$\left[ML{T}^{-2}\right]\left[L{T}^{-2}\right]=constant$

$L^2{T}^{-3}=constant(\because massisconstant)$

$L\propto T^{\frac{3}{2}}$

$\Rightarrow Displacement\left(d\right)\propto t^{\frac{3}{2}}$


Final Answer: (𝑏)