Question

A particle at rest is moved along a straight line by a machine giving constant power. The distance moved by the particle in time ‘$t$’ is proportional to

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

Answer 1

Answer: (D)

Power, $P=\text{ Force }\times \text{ Velocity }$
$=F\times v$
$=ma\times v=$constant
So, $va=$ constant
$v\frac{dv}{dt}=$ constant
Integrating it, we have
$\frac{v^2}{2}=Ct$
or$v=\sqrt{2Ct}=C_1{t}^{1/2}$
or $\frac{dx}{dt}=C_1{t}^{1/2}$
Integrating it, we get
$x=C_2{t}^{3/2}$
So$x\propto t^{3/2}$