Question

Define kinetic energy. Derive an expression for it.

Answer 1

Definition of Kinetic energy

Kinetic energy is defined as the energy possessed by a moving body due to its motion.

The formula for Force and Work done

As per Newton's law of motion, $F=ma$ where F = Force, m = mass, a = acceleration.

Work = $Fs$ where s = displacement

Applying Newton's law of motion, Work = $mas$

Deriving the equation

From the equation of motion, $v^2-u^2=2as$

As the body is initially at rest $\left(u=0\right)$, hence $v^2=2as$ or $\frac{v^2}{2}=as$

Applying this to the work formula,

Work = $mas=m\left(\frac{v^2}{2}\right)=\frac{1}{2}m{v}^2$

Hence, Kinetic energy = $\frac{1}{2}m{v}^2$