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# Derive the expression for kinetic energy. [5 MARKS]

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Solution

## Each point: 1 Mark 1. By definition we can say that the kinetic energy of 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 F s. 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 v2 - u2=2as s=v2−u22a 3. We know F=ma and work done =F×s; W=ma×v2−u22a W=m(v2−u2)2 4. If the starting velocity of the object is zero, then u = 0; Work done will be = 12mv2 5. Thus the kinetic energy of the object having mass m and the velocity of the object is v. Then kinetic energy is = 12mv2

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