Question

A particle at rest is moved along a straight line by a machine giving constant power. The distance moved by the particle in time ‘$t$’ is proportional to

• A. $t^{\frac{1}{2}}$
• B. $t^{\frac{2}{3}}$
• C. $t$
• D. $t^{\frac{3}{2}}$

Answer 1

Answer: (D)

Power, $P =\text { Force } \times \text { Velocity } $
$=F \times v $
$=m a \times v=$constant
So, $ \,\,\,v a=$ constant
$v \frac{d v}{d t}=$ constant
Integrating it, we have
$\frac{v^{2}}{2} =C t $
or$\,\,\,v =\sqrt{2 C t}=C_{1} t^{1 / 2}$
or $\,\,\,\frac{d x}{d t}=C_{1} t^{1 / 2}$
Integrating it, we get
$x=C_{2} t^{3 / 2} $
So$\,\,\,\,x \propto t^{3 / 2}$