Question

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

• A. $4$
• B. $2$
• C. $1$
• D. $5$

Answer 1

The correct option is D

$5$

Step 1: Given data.

Mass of the particle, $m=0.2kg$

Power, $P=0.5w$

Step 2: Finding the final speed of the particle after $5s$.

We know that,

According to the work-energy theorem

$W=KE$

Where $W$ is work done and $KE$ is Kinetic energy.

$W=\frac{1}{2}m{v}^2$ $\left[\because KE=\frac{1}{2}m{v}^2\right]$ ……$\left(i\right)$

Also,

$W=$Power $\times$time

$\Rightarrow$ $W=P\times t$

$\Rightarrow$$\frac{1}{2}m{v}^2=P\times t$ $\left[\because fromequation\left(i\right)\right]$

$\Rightarrow$ $v=\sqrt{\frac{2Pt}{m}}$

$\Rightarrow$ $v=\sqrt{\frac{2\times 0.5t}{0.2}}$

At $t=5s$

$v=\sqrt{\frac{2\times 0.5\times 5}{0.2}}$

$\Rightarrow$$v=5\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Hence, option D is correct.