Question:
A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time ' $t$ ' is proportional to:
Correct Option: 1
Solution:
$\mathrm{P}=$ constant
$\frac{1}{2} \mathrm{mv}^{2}=\mathrm{Pt}$
$\Rightarrow \mathrm{v} \propto \sqrt{\mathrm{t}}$
$\frac{d x}{d t}=C \sqrt{t}$ $\mathrm{C}=\mathrm{constant}$
by integration.
$\mathrm{x}=\mathrm{C} \frac{\mathrm{t}^{\frac{1}{2}+1}}{\frac{1}{2}+1}$
$x \propto t^{3 / 2}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.