Question

prove the expression for kinetic energy

Answer 1

Let a body of mass ‘m’ is moving with a velocity ‘v’.A force ‘F’ is applied on it to stop its motion for which the retardation ‘h’ is produce in the body and the body covers a distance ‘s’ before coming rest.

Work done by the force to stop the motion of the body is the measure of kinetic energy .

Here

Initial velocity = v

Final velocity = 0(zero)

From Newton’s 2nd law

F = ma

or, a = F/m

From 3rd equation of motion

0=v^2 - 2as

or, 2as = v^2

or, 2 × F/m × s = v^2

or, s = (mv^2) /2F

Therefore , workdone by the force,

W = Fs

or, W = F ( mv^2 )/2F

or, W = 1/2 mv^2

Hence,

Kinetic energy = 1/2mv^2

PLEASE GIVE ME BRAINLIEST.

Answer 2

suppose, a stationary object of mass m moves with the applied force. let u be initial velocity (here u= 0). let the applied force be F. This generates an acceleration a in the object, and, after time t, the velocity of object becomes equal to v. The displacement during this time is s. Teh work done on the object, W= F×s.

According to Newton's second law of motion,

F= ma.......(1) similarly using Newton's second law of motion.

s= ut+ ½ at².......However as, initial velocity is zero.

s= 0+ ½ at².

s= ½ at²........(2)

W= ma ½ at²........using equations (1) and (2)

W= ½ m (at)².......(3)

Using Newton's first equation of motion.......

v= u+at

v= 0+ at

v= at

(v)²= (at)²..........(4)

W= ½ mv²........using equations (3) and (4)

The kinetic energy gained by an object is the amount of work doneon the object.

K.E= W

K.E= ½ mv²