Question

A particle of mass 10 kg is moving with velocity of $10\sqrt{x}m/s,$ where x is displacement. The work done by net force during the displacement of particle from $x=4m$ $x=9m$ is

• A. 1250 J
• B. 1000 J
• C. 3500 J
• D. 2500 J

Answer 1

The correct option is D 2500 J

Given that

$m=10kg$

1. $v=10\sqrt{x}$ m/s and $\frac{dv}{dx}=\frac{5}{\sqrt{x}}$

We know that

$W=ma=m\frac{dv}{dt}=m\frac{dv}{dt}\frac{dx}{dx}=mv\frac{dv}{dx}$

Hence

$W={\int }_{x_1}^{x_2}mvdv={\int }_4^{9}10\times 10\sqrt{x}\frac{5}{\sqrt{x}}dx=500[x{]}_4^9=500(9-4)=2500J$