Kinetic Energy

Kinetic energy is the energy a body possesses by virtue of its motion and is given by $K=\frac{1}{2}m{v}^2$, where $m$ is the mass and $v$ the speed. It is a scalar quantity that scales linearly with mass but quadratically with speed, which is why doubling speed quadruples the energy. Substituting $m=2\text{ kg}$ and $v=10\text{ m/s}$ yields $K=\frac{1}{2}(2)(10{)}^2=\frac{1}{2}(2)(100)=100\text{ J}$. The option 200 J forgets the factor of one-half. The option 20 J incorrectly uses $v$ linearly instead of $v^2$. The option 50 J halves the mass contribution without justification. This is the standard NCERT relation for the kinetic energy of a point mass. As a sanity check, the joule is equivalent to $\text{kg}{\text{m}}^2/{\text{s}}^2$, and $2\times 10^2/2=100$ reproduces both the correct units and magnitude expected for an everyday thrown ball.