Work Power Energy Question 6
Question 6 - 30 January - Shift 2
A body of mass $2 \mathrm{~kg}$ is initially at rest. It starts moving unidirectionally under the influence of a source of constant power $P$. Its displacement in $4 s$ is $\frac{1}{3} \alpha^{2} \sqrt{P} m$. The value of $\alpha$ will be
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Answer: (4)
Solution:
Formula: Relation between Momentum and Kinetic Energy
$\frac{1}{2} mV^{2}=Pt$
$V=\sqrt{\frac{2 Pt}{m}}$
$\frac{dx}{dt}=\sqrt{\frac{2 Pt}{m}}$
$x=\sqrt{\frac{2 P}{m}} \frac{2}{3}[t^{3 / 2}]_0^{4}$
$x=\frac{16 \sqrt{P}}{3}=\frac{1}{3} \times 16 \sqrt{P}$
$\alpha=4$
