Question

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

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

Answer 1

Answer: (B)

Power is defined as amount of work done per unit time.
Power is defined as time rate of doing work
i.e., $P=\frac{dW}{dt}$
Also work down $=$ force $\times$ displacement $=F.d$
and force $=$ mass $\times$ acceleration $=ma$
$\therefore P=\frac{Fd}{t}=\frac{ma\cdot d}{t}$
Also, distance $=$ speed $\times$ time
i.e., $d=vt\Rightarrow v=\frac{d}{t}$
and acceleration, $a=\frac{v}{t}$
$\therefore P=\frac{m}{t^2}vd$
$P=\frac{m}{t^2}\cdot \frac{d}{t}\cdot d=\frac{m{d}^2}{t^3}$
$\Rightarrow d^2\propto t^3$
$\Rightarrow d\propto t^{3/2}$