Question

A block of mass 2 kg is initially at rest on a horizontal frictionless surface. A horizontal force $\vec{F}=\left(9-x^2\right)\hat{i}N$ acts on it, when the block is at $x=0$. The maximum kinetic energy of the block between $x=0$ and $x=3m$ in joule is

• A. $24$
• B. $20$
• C. $18$
• D. $15$

Answer 1

Answer: (C)

From work-energy theorem kinetic energy of the block at $x=x$ is
K=$\underset{0}{\overset{x}{\int }}$$\left(9-x^2\right)dx=\left[9x-\frac{x^3}{3}\right]$
For $K$ to be maximum, $\frac{dK}{dx}=0$
or $9-x^2=0$ or $x=\pm 3m$
At $x=+3m\frac{d^{2}K}{d{x}^2}$ is negative
i.e., Kinetic energy $K$ is maximum.
$\therefore K_{max}=9\left(3\right)-\frac{{\left(3\right)}^3}{3}=18J$