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 =1/2mv^2

Answer 2

Kinetic energy of an object is defined as the energy that it possesses due to its motion.

It is also described as the work required to accelerate a body of a given unit of mass from rest to its stated velocity.

Derivation:

Let us consider an object of mass " m " upon which Force "F" is acting and let the object from rest move from point A to point B to cover a displacement "S".

We know,

Work done = Force x displacement

W= FxS ____(1)

An equation of motion--- V^2 -U^2 =2aS

S= V^2 -U^2/2a ______(2)

Newtons second law of motion--- F= ma

We derive from equation 1 and 2,

W= m*a* (V^2- U^2)/2a

u=0 as object is at rest

W=m*V^2/2

WORK Done is the kinetic energy of the body.

K.E = (1/2 )mv^2