# obtain an expression for kinetic energy of a body moving uniformly

1
by ajitparmar

2015-12-13T10:37:05+05:30
Kinetic energy=1/2mv^2 V here is constant as body moves uniformly
Suppose, the mass of a moving object = m

The initial velocity of a moving object = u

The acceleration of the object = a

The final velocity of the object = v

Displacement of object to achieve the final velocity = s.

We know from the equation of motion that,

Work and Energy1
Now, we know that, Work done, W = F x s

Thus, by substituting the value of ‘s’ from equation (i) in the expression W = F x s, we get

Work and Energy2
Now, according to Newton’s Second Law of motion, Force = mas
Force = mass x acceleration

Or, F = m x a

Therefore, by substituting the value of F in equation (ii) we get,

Work and Energy3
If the object starts moving from the state of rest, therefore, initial velocity (u) will be equal to zero.

Therefore, equation (iii) can be written as

Work and Energy4
Equation (iv) shows that work done is equal to the change in kinetic energy of an object.

Therefore, if an object of mass ‘m’ is moving with a constant velocity,

Work and Energy5