Question

A particle of mass $0.2\text{kg}$ is moving in one dimension under a force that delivers a constant power of $0.5\text{W}$ to the particle. If the initial speed (in ${\text{ms}}^{-1}$) of the particle is zero, then the speed (in ${\text{ms}}^{-1}$) of the particle after $5\text{s}$ is:

• A. $8$
• B. $5$
• C. $15$
• D. $25$

Answer 1

The correct option is B $5$

Given, mass of particle $m=0.2\text{kg}$
$\text{Power}=\frac{\text{Work done}}{\text{Time Interval}}$
$\Rightarrow P=\frac{W}{t}$
$\therefore$Work done by external force on the particle in time interval of $5\text{s}$
$W=P.t=0.5\times 5=2.5\text{J}$

As mentioned in question, given force is the only external force acting on system.
So, from Work-energy theorem,
$W_{\text{ext}}=\Delta KE$
$W=K{E}_f-K{E}_i=\frac{1}{2}m{v_f}^2-0$
$\Rightarrow 2.5=\frac{1}{2}\times \left(0.2\right)\times {v_f}^2$
$\therefore v_f=\sqrt{25}=5\text{m/s}$

Hence $v_f=5\text{m/s}$ is the speed after $5\text{s}$