Question

Derive an expression for kinetic energy possessed by an object of mass m moving with velocity v. also state si unit of kinetic energy.

Answer 1

Consider a body of mass "m" moving with an initial velocity "u".
A constant force "F" acts on it and the velocity changes to "v".

Let "s" be the distance covered and "a" be the constant acceleration


We know that

v² - u² = 2as

s = $\frac{v^{2} - u ^{2} }{2a}$


We know that ,

Work done = Force(F) × displacement (s)

F = ma


W = ma ×$\frac{v^{2} - u ^{2} }{2a}$


["a" gets cancelled ]

W = m ×$\frac{v^{2} - u ^{2} }{2}$
= $\frac{1 }{2}$ m[v² - u² ]


When , initial velocity , u = 0

W = $\frac{1 }{2}$ mv²

K.E = Work done
= $\frac{1 }{2}$ mv²

Answer 2

Kinetic Energy:
The energy possessed by an object due to its motion is called as kinetic Energy.
Derivation:
Let us consider an object of mass " m " 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 on the object is :
Workdone = Force x displacement.
W= FxS ____(1).
From third equation of motion;
V^2 -U^2 =2aS
S= V^2 -U^2/2a ______(2)
By Newtons second law of motion:
F= ma
From equation 1 and 2
W= m*a* (V^2- U^2)/2a
As we have assumed object is at rest, u=0
W=m*V^2/2
The WORK Done appears as kinetic energy of the body.
Therefore,
K.E = (1/2 )mv^2