Question

Derive an expression K.E = ½ mv2 for a freely falling body of mass m.​

Answer 1

Answer:

IF 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

Explanation:

First of all we will find the acceleration of body.

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

Answer:

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.

Please see attachment for further answer.

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