Question

A constant power is delivered to a body moving along a straight line. the distance travelled by the body in time t is proportional to

• A. $t^{1/2}$
• B. $t^{3/2}$
• C. $t^{5/2}$
• D. $t^{7/2}$

Answer 1

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

$\begin{array}{c}powerP=Fv=mav\\ accelerationa=\frac{S}{t^2}andvelocityv=\frac{S}{t},\\ whereSisthedis\tan cemoved\\ SincethepowerPandmassmarecons\tan t,weget\\ P=\frac{mS}{t^2}\times \frac{S}{t}\to S^2=t^2\to S\propto t^{\frac{3}{2}}\end{array}$

Hence,

option $B$ is correct answer.