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 $x = 3\,m$ 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=$\int\limits^{x}_{{0}}$$\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 $x=\pm3\,m$
At $x=+3\,m \frac{d^{2}K}{dx^{2}}$ is negative
i.e., Kinetic energy $K$ is maximum.
$\therefore K_{max}=9\left(3\right)-\frac{\left(3\right)^{3}}{3}=18\,J$