(a) Derive the mathematical expression for the kinetic energy of an object moving with a
uniform acceleration.
Answers
Derive the mathematical expression for the kinetic energy of an object moving with a
uniform acceleration.
Explanation:
Kinetic Energy can be defined as the energy possessed by an object due to its motion.
In order to derive:
We will consider an object of mass "n " which is at rest on smooth horizontal plane.
Let a Force , F acts on the object and let the object from rest moves from point A to point B and covers a displacement S.
The work done by force (F) on the object will be:
Work-done = Force x displacement.
W= F*S ......................(a)
From third equation of motion;
V² -U² =2aS
S= V² -U²/2a ..............(b)
By Newtons second law of motion:
F= na
From a and b we get ;
W= n*a* (V²- U²)/2a
We will assume that the object is at rest, u=0
W=n*V²/2
The work done appears as thekinetic energy of the body.
∴,
K.E = (1/2 )nv²