Question

state and derive the expression of kinetic energy​

Answer 1

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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= $\frac{ {v}^{2} }{2a}$

Work done F∗s

=mas=ma $\frac{ {v}^{2} }{2a}$

Work done = $\frac{1}{2} {mv}^{2}$

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

∴ kinetic energy of the body, Ek=$\frac{1}{2} {mv}^{2}$