Question

Define Kinetic energy and derive an expression for Kinetic energy where sysmbol have their usual meaning.

Answer 1

Kinetic energy:- Energy possessed by a body by virtue of its motion is called kinetic energy.

$Derivation-$

Consider a body of mass $m$ initially at rest, and on application of force $F$, it travels a distance $s$ then the work done is given by

$W=F\times s$. . . . .(1)

By Newton's second law,

$F=ma$. . . . . . . . (2)

where, $a=$ acceleration

3rd equation of motion,

$v^2-u^2=2as$

$v^2=2as$

$a=\frac{v^2}{2s}$. . . .(3)

Substitute equation (2) and (3) in equation (1), we get

$W=m\times \frac{v^2}{2s}\times s$

$W=\frac{1}{2}m{v}^2$

This work done is stored as a kinetic energy.

The expression for kinetic energy is given by

$K.E=\frac{1}{2}m{v}^2$