Question

Obtain an expression for K.E. of a body moving uniformly?
CLASS - XI PHYSICS (Work, Energy and Power)

Answer 1

We know that
v^2 = u^2 + 2aS
v= final velocity
u= initial velocity
a= acceleration due to gravity
S = displacement
S= (v^2 - u^2)÷2a
Work done= force * displacement
W = F * S
F= ma
W= ma * (v^2 - u^2)÷2a
W= 1/2 * m* (v^2-u^2)
If u=0 ( body starts from rest)
W= 1/2 * m * v^2=Kinetic energy

Hope this helps

Answer 2

Kinetic energy is the energy possesed by the body by virtue of its motion.
K.E= 1/2 m V^2

Derivation:

Consider an object with mass m at rest ( u=0) . A force F acts on an object and it moves through a distance s.
According to Work done
W= Fxd
= Fxs
From Newton's second law F= ma
W= maS----------(1)
From third equation of motion:
V^2 - U^2 = 2as
S= V^2 -U/2 /2a
Substituting the value of s in equation 1 we get:
W= ma ( V^2 -U/2) /2a
=m ( V^2 -U^2)/2
Since u=zero.
W= mV^2/2
SINCE Work done on an object is stored as K.E

K.E= 1/2 mV^2