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., $P=\frac{d W}{d t}$
Also work down $=$ force $\times$ displacement $=F. d$
and force $=$ mass $\times$ acceleration $=m a$
$\therefore P=\frac{F d}{t} =\frac{m a \cdot d}{t}$
Also, distance $=$ speed $\times$ time
i.e., $d=v t \Rightarrow v=\frac{d}{t}$
and acceleration, $a=\frac{v}{t}$
$\therefore P=\frac{m}{t^{2}} v d$
$P=\frac{m}{t^{2}} \cdot \frac{d}{t} \cdot d=\frac{m d^{2}}{t^{3}}$
$\Rightarrow d^{2} \propto t^{3}$
$\Rightarrow d \propto t^{3 / 2}$