Question

A body is moving and directionally under the influence of a source of constant power. It's displacement in time t is proportional to

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

Answer 1

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

Power , $Power=force\times velocity$

$P=F\times v$

$P=ma\times v$. . . . . .(1)

From 1st equation of motion,

$v=u+at=at$ Initially starts with rest.

Equation (1) becomes,

$P=m{a}^{2}t$

$a=\sqrt{\frac{P}{mt}}$

From 2nd equation of motion,

Displacement, $S=ut+\frac{1}{2}a{t}^2$

$S=\frac{1}{2}.\sqrt{\frac{P}{mt}}.t^2=\sqrt{\frac{P}{m}}.t^{3/2}$

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

The correct option is C.