Question

A particle of mass $0.2\text{kg}$ (initially at rest) starts moving in one dimension under a force that delivers a constant power $0.5W$ to the particle. Then the speed after $5\text{seconds}$ is

• A. $20\text{m/s}$
• B. $5\text{m/s}$
• C. $10\text{m/s}$
• D. $20\text{m/s}$

Answer 1

The correct option is B $5\text{m/s}$

Given, Mass of the particle $m=0.2\text{kg}$
Power $P=0.5W$
Initial speed $u=0m/s$

We know that, Power $P=Fv$
[when force and velocity are in same direction]

$P=ma\times v=mv\frac{dv}{dt}$
$\Rightarrow 0.5=mv\frac{dv}{dt}$ [$P=0.5W$, given]
or $mvdv=0.5dt$
Integrate on both sides,
${\int }_0^{v}mvdv={\int }_0^{5}0.5dt$
[let velocity after $5s$ be $v$]
$\Rightarrow \frac{m{v}^2}{2}=0.5\times 5$
$\Rightarrow v=\sqrt{\frac{0.5\times 5\times 2}{0.2}}$
$\therefore v=5\text{m/s}$