Question

Derive the formula for the kinetic energy of an object of mass m, moving with velocity v .

Answer 1

Kinetic energy is the energy possessed by an object by virtue of its motion.
K.E=1/2 mV²

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=FxS
W=FnetXS-------(1)
Let the workdone 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*(V²-u²/2a)\=(1/2)m(V²-u²)
As we assumed object at rest, u=0
W=(1/2)mV²
we know that the kinetic energy of a body moving with certain velocity is equal to workdone on the object to acquire that velocity from rest.
∴K.E=1/2 mV²