Question

Power supplied to a particle of mass $5\text{kg}$ varies with time as $P=\frac{4t^3}{5}\text{W}$, where $t$ is in $\text{seconds}$. If the velocity of the particle at $t=0$ is zero, then what will be the velocity of the particle at $5\text{seconds}$?

• A. $5\sqrt{2}\text{m/s}$
• B. $\sqrt{2}\text{m/s}$
• C. $5\text{m/s}$
• D. $2\text{m/s}$

Answer 1

The correct option is A $5\sqrt{2}\text{m/s}$

From Work energy theorem, we have
$\Delta KE=W_{net}$
$⟹K_f-K_i=\int P.dt$
$⟹\frac{1}{2}m{v}^2-\frac{1}{2}m\times (0{)}^2={\int }_0^5\frac{4t^3}{5}dt$
$⟹\frac{1}{2}m{v}^2=\frac{4t^4}{4\times 5}{|}_0^5$
​​​​​​​$⟹\frac{1}{2}\times 5\times v^2=\frac{625}{5}$
​​​​​​​$⟹v^2=25\times 2$
​​​​​​​$⟹v=5\sqrt{2}\text{m/s}$