Question

b. Derive the formula for the kinetic
energy of an object of mass m.
moving with velocity v.
​

Answer 1

Let the initial velocity of the object be u. Let an external force be applied on it so that it gets displaced by distance s and its velocity becomes v. In this scenario, the kinetic energy of the moving body is equal to the work that was required to change its velocity from u to v.

Answer 2

Answer:

Consider a body of mass m moving with a uniform acceleration a along a straight line. If u is the initial velocity of the body, v is the final velocity and s is the distance covered by the body during this change of velocity, we have

v²=u²+2as (the kinematical equation of motion)

v²=u²=2as

s=v²-u²

_____

2a ...(1)

If F is the net force acting on the body and W is the work done by the force,

W=Fs ...(2)

Now, F = ma ...(3)

From Eqs.(1),(2) and (3), we get,

W=ma × v²-u² 1

____ =__m (v²-u²)

2a 2

For a body initially at rest, u=o

W=1

_ mv²

2

Work done on a body = change in the kinetic energy of the body.

Kinetic energy of the body 1

_ mv²

2