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

Answer 1

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

Power, $P=$ Force $\times$ 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, $x\propto t^{3/2}$