Question

Derive the expression for kinetic energy. [5 MARKS]

Answer 1

Each point: 1 Mark

1. By definition we can say that the kinetic energy of a moving body at the given velocity is equal to work done on it to acquire that velocity.

2. Let’s consider an object of mass, m moving with a uniform velocity, u. Let it now be displaced through a distance s when a constant force, F acts on it in the direction of its displacement.

The work done, W is Fs. The work done on the object will cause a change in its velocity. Let its velocity change from u to v. Let a be the acceleration produced. We studied three equations of motion. The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, s is

$v^2$ - $u^2=2as$

$s=\frac{v^2-u^2}{2a}$

3. We know $F=ma$ and work done =$F\times s$;

$W=Fs=ma\times \frac{v^2-u^2}{2a}$

$W=\frac{m(v^2-u^2)}{2}$

$WD=\frac{1}{2}m(v_f^2-v_i^2)$

4. If the starting velocity of the object is zero, then u = 0;
Work done will be = $W=\frac{1}{2}m{v}^2$

5. Thus the kinetic energy of the object having mass m and the velocity of the object v is = $\frac{1}{2}m{v}^2$.