Question

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $t$ proportional to

• A. $\sqrt{t}$
• B. $t^{3/4}$
• C. $t^{3/2}$
• D. $t^2$

Answer 1

The correct option is C $t^{3/2}$

$Power=\frac{K.E}{time}=\frac{\frac{1}{2}m{v}^2}{t}=Constant$

So, $\frac{v^2}{t}=Constant$

$\Rightarrow v=\sqrt{Ct}$

$v=K{t}^{1/2}$

$\frac{dx}{dt}=K{t}^{1/2}\Rightarrow dx=K{t}^{1/2}dt$

Integrating both side

$x=\int K{t}^{1/2}dt$

$x=\frac{K{t}^{3/2}}{3/2}+C$

$\Rightarrow x\propto t^{3/2}$