Question

Derive an expression for Kinetic energy possessed by an object of mass m, moving with
a velocity v.

Answer 1

Consider a body of mass "m" starts moving from rest. After a time interval "t" its velocity becomes V.

If initial velocity of the body is Vi = 0 ,final velocity Vf = V and the displacement of body is "d". Then

Using equation of motion

2aS = Vf2 – Vi2

Putting the above mentioned values

2ad = V2 – 0

a = V2/2d

Now force is given by

F = ma

Putting the value of acceleration

F = m(V2/2d)

As we know that

Work done = Fd

Putting the value of F

Work done = (mv2/2d)(d)

Work done = mV2/2

OR

Work done = ½ mV2

Since the work done is motion is called "Kinetic Energy"

i.e.

K.E. = Work done

OR

K.E. =1/2mV2.

Answer 2

refer to the attachment above.........