Question

What is kinetic energy? Derive an equation for the kinetic energy of a body of mass '$m$' moving at a speed '$v$'.

Answer 1

Kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.

Derivation:

Let us consider an object of m which is at rest lying on a table.

Let A force F acts on the object which moves the object through a distance S.

The workdone$=F\times S$

$W=F_{net}\times S$-------(1)

Let the work done on the object causes a change in its velocity from u to V and let a be the acceleration.

From Third equation of motion:

$V²-u²=2as$

$s=V²-u²/2a$----------(2)

By Newton's Second law:

$F=ma$------(3)

From equation (1), (2) and (3)

$W=ma\times (V^2-u^2/2a)=\left(1/2\right)m(V^2-u^2)$

As we assumed object at rest, $u=0$

$W=\left(1/2\right)m{V}^2$

we know that the kinetic energy of a body moving with a certain velocity is equal to work done on the object to acquire that velocity from rest.

$\therefore K.E=1/2m{V}^2$