Question

A block of mass 2 kg is initially at rest on a horizontal frictionless surface. A horizontal force $\overrightarrow{F}=(9-x^2)\hat{i}$ 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

The correct option is C $18$

Max K.E will at the point where $v$ is max i.e$a=\frac{dv}{dt}=0$

$\Rightarrow F=0$

$F=0$ when $x=3$

Work done is the change in KE.

$W=\Delta K.E={\int }_0^3(9-x^2)dx=[9x-\frac{x^3}{3}{]}_0^3=18J$