Question

Deduce the unit of kinetic energy of a body using the expression for work done by a constant force acting

on it.
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Answer 1

Answer:

Kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.

Derivation: 

Let us consider an object of m which is at rest lying on a table.

Let A force F acts on the object which moves the object through a distance S.

The workdone=F×S

W=Fnet×S-------(1)

Let the work done on the object causes a change in its velocity from u to V and let a be the acceleration.

From Third equation of motion:

V²−u²=2as

s=V²−u²/2a----------(2)

By Newton's Second law:

F=ma------(3)

From equation (1), (2) and (3)

W=ma×(V2−u2/2a)=(1/2)m(V2−u2)

As we assumed object at rest, u=0

W=(1/2)mV2

we know that the kinetic energy of a body moving with a certain velocity is equal to work done on the object to acquire that velocity from rest.

∴K.E=1/2mV2