Question

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $t$ is proportional to :

• A. $t^{3/4}$
• B. $t^{3/2}$
• C. $t^{1/4}$
• D. $t^{1/2}$

Answer 1

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

Let's consider a body is moved along a straight line by a machine delivering a constant power $P$. The distance moved by the body is $S$.

Power, $P=F.v$.. . . . . . (1)

Force, $F=ma$ . . . . . . . .(2)

where, $v=\frac{S}{t}$

acceleration, $a=\frac{S}{t^2}$

$m=$ mass

from equation (1) and equation (2), we get

$P=\frac{mS}{t^2}\times \frac{S}{t}$

$S^2=\frac{P{t}^3}{m}$

From the above equation, we get

$S^2\propto t^3$

$S\propto t^{3/2}$

The correct option is B.