Question

using equations of motion, derive an expression for kinetic energy of a body.
​

Answer 1

Answer:

Suppose a body of mass m is moving with velocity v. It is brought to rest by applying a retarding force F. Suppose it traverses a distance s before coming to rest. Kinetic energy of body, KE = Work done by retarding force to stop it.

Answer 2

Answer:

Consider a body of mass ‘m’ at rest. Let a constant force F act on the body producing an

acceleration ‘a’ for a distance ‘s’. Let the velocity of the body be changed to v.

In this case, initial velocity =0.

Final velocity =v.

Using, v

2

=u

2

+2as

v

2

=0+2as

v

2

=2as

s=

2a

v

2

Work done F∗s

=mas=ma

2a

v

2

Work done =

2

1

mv

2

By definition this work done is equal to the kinetic energy.

∴ kinetic energy of the body, E

k

=

2

1

mv

2

.