Question

derive an expression for Kinetic Energy of a body in motion ​

Answer 1

Explanation:

Let there be an object of mass, m at rest, i.e. initial velocity, u = 0

From Newton’s Ilnd Law of Motion, we have v2 – u2 = 2as

Where, v = Final velocity; u = Initial velocity; s = Displacement of an object ,a = Acceleration

Let the object at rest be moved by displacement, s.

Let ‘v’ be the final velocity on moving the object, and ‘a’ be the acceleration produced.

Now, from Newton’s IIIrd Law of Motion, we know that force acting on the object,

W = F.s

Or,

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

Or,

$w = ma \times ( \frac{ {v}^{2} }{2a} )$

Or,

$w = \frac{m {v}^{2} }{2}$

Here, work done is equal to the change in the kinetic energy of the object.

Kinetic Energy, K.E. = (1/2)mv^2