(i) Derive an expression for the kinetic energy of an object. Write the SI unit of kinetic energy. (ii) An object of mass 10 kg is moving with a uniform velocity of 5 m s^-1. Calculate the kinetic energy possessed by the object

(i) Consider a body of mass m initially lying at rest i.e., u = 0 on a perfectly frictionless surface. Let a constant force F be acting on the body, such that the acceleration produced in the body is ‘a’. Let the body possess a velocity V after undergoing a displacement ‘S’, then by the equation of motion
v^2- u^2 = 2aS, we have
a = v^2 / 2S …(i)
Now, the work done by the force in displacing the body through a distance S is given by
W = F x S …(ii)
Since the force and displacement are in the same direction, therefore, we have
W = FS = maS = m x v^2/2S x S = 1/2 mv^2 …(iii)
This work done to put the body in motion is stored in the body as its kinetic energy. Hence, the kinetic energy of the body is K = 1/2 mv^2. …(iv)
Thus, the kinetic energy of a body is directly proportional to its mass and square of its velocity. Its SI unit is joule.

(ii) Mass of the object, m = 10 kg, velocity of the object, v = 5m s^-1
KE = 1/2 mv^2 = 1/2 x 10 x (5)^2 = 125 J