Question

A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time $t$ is proportional to

• A. $t^2$
• B. $t^{\frac{3}{2}}$
• C. $t$
• D. $t^{\frac{1}{2}}$

Answer 1

The correct option is B $t^{\frac{3}{2}}$

Using dimensional analysis, we can verify this.

$P=F\times v$

So, writing the dimensions for the quantities on right hand side we get,
$P=\left[ML{T}^{-2}\right]\left[L{T}^{-1}\right]=\left[M{L}^2{T}^{-3}\right]$

Since, dimensions of $P=\left[M{L}^2{T}^{-3}\right]=\text{constant}$

i.e. $\left[L^2{T}^{-3}\right]=\text{constant},\frac{L^2}{T^3}=\text{constant}$

This gives us, $L^2\propto T^3$

Therefore, $L\propto T^{3/2}$

So, option $\left(C\right)$ is the correct answer.