Question

Derivation of 1/2mv2?

Answer 1

w. k. t
work = force * displacement. (1)
force = mass * acceleration
=MA. (2)
displacent :
2as=v^2-u^2
s=v^2-u^2/2a. (3)
substituting eq. (2)2 and (3) in (1) we get
f=ma*v^2-u^2/2a
a gets cancelled
we get
m(v2-u2) /2
=1/2 *m(v^2-u^2)
if the object starts from rest then u=0 so, 0^2=0
so
1/2 *m(v^2)

Answer 2

Hey friend,

Here's your answer,


EXPRESSION OF KINETIC ENERGY


Consider a body of mass m lying at rest on a smooth floor. Let a force F be applied on the body so that the body attains a velocity v after travelling a distance S

Therefore,

Work done by the force on the body, W = FS (Eqn 1)


Since the velocity of the body changes from zero to v, so the body is accelerated. Let a be acceleration of the body. Then, according to Newton's second law of motion,


F = ma

Substituting the value of F = ma in eqn 1, we get,


W = (ma)S (Eqn 2)


Now,
Using,

V2 - u = 2aS,

We get,


v² - 0 = 2aS, or

S = V2 / 2a (Eqn 3)


Substituting the value of S from eqn 3 in eqn 2,

We get,


W = ma × v² / 2a = ½ mv². (Eqn 1)

This work done is equal to the kinetic energy of the body.

Therefore,

Kinetic energy,

K = ½ mv². (Eqn 2)


Or,

K = ½ (mass of the body) (speed of body)²


K.E. of a body is directly proportional to :-

1. Its mass

2. Square of it's speed.



Hope this helps!!!