Question

A particle of mass $0.2\text{kg}$ is moving in one dimension under a force that delivers a constant power $0.5\text{W}$ to the particle. If the initial speed (in $\text{m/s})$ of the particle is zero, then speed in $\left(\text{m/s}\right)$ after $5\text{s}$ is

• A. $2.5\text{m/s}$
• B. $5\text{m/s}$
• C. $10\text{m/s}$
• D. $3\text{m/s}$

Answer 1

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

Given, mass of particle $m=0.2\text{kg}$
Power $=0.5\text{W}$
Work done$\left(w\right)=F.d$
Assume, displacement of particle is $d$
Final speed of the particle $=v$
Applying kinematic equation,
$v^2=u^2+2ad$
$v^2=0+2ad$
or $v^2=2ad...\left(i\right)$

$\because F=ma$
Work done $w=F.d=ma.d$
$\Rightarrow w=\frac{m}{2}\left(2ad\right)....\left(ii\right)$

From Eq $\left(i\right)$ and $\left(ii\right)$,
Work done $\left(w\right)=\frac{m}{2}{v}^2...\left(iii\right)$
Power $P=\frac{dw}{dt}$
$\Rightarrow {\int }_0^{w}dw={\int }_0^{5}Pdt$
$\Rightarrow w={\int }_0^{5}0.5dt=0.5{\left[t\right]}_0^5$

From Eq $\left(iii\right)$,
$\frac{0.2v^2}{2}=0.5\times 5$
$\therefore v=\sqrt{25}=5\text{m/s}$