Question

The power supplied by a force acting on a particle moving in a straight line is constant . The velocity of the particle varies with the displacement $x$ as

• A. $x^{1/2}$
• B. $x$
• C. $x^2$
• D. $x^{1/3}$

Answer 1

Answer: (D)

$x^{1/3}$

$p=Fv=\left(ma\right)v$
$m=\left(\frac{d^{2}x}{d{t}^2}\right)\left(\frac{dx}{dt}\right)$
Since,power is constant
$\left(\frac{d^{2}x}{d{t}^2}\right)\left(\frac{dx}{dt}\right)=k$
$\frac{d}{dx}(\frac{dx}{dt}{)}^2=k$
$(\frac{dx}{dt}{)}^2=k_{1}t$
$\frac{dx}{dt}=\sqrt{k_{1}t}$
$\frac{dx}{dt}=k_2(t{)}^{1/2}$
$x=k_3{t}^{3/2}$
$\frac{dx}{dt}\alpha t^{1/2}\alpha x^{1/3}$