Question

derive the expression for kinetic energy

Answer 1

Question

Derive the expression for kinetic energy.

Explanation of Basic Terms

Work - The maginitude of the force multiplied by the distance travelled moved by the object/body in the direction of applied force.

Energy - The ability to do work.

Kinetic Energy - The energy possessed by a moving object/body.

Expression for Kinetic Energy

Consider a body of mass 'm' having Initial velocity 'u'. Let it now be displaced through a distance 's'. when a constant force 'f' acts on it. Let it's velocity change from 'u' to 'v'.

Therefore work done by the Object is W = F × S

[The following steps need not be included in the derevation. It has been written fo you to understand it better.]

We know that,

F = ma → 1

Lets now derive an equation for 's' to substitute it in the formula for Work Done.

From equations of Motion,

v² - u² = 2as

$\mathsf{\frac{v^{2} - u^{2} }{2a}}$ = s → 2

Now, lets go back to the formula for Work Done.

W =  F × S

From 1 and 2,

W = ma × $\mathsf{\frac{v^{2} - u^{2} }{2a}}$

[a gets cancelled on both sides]

W = m × $\mathsf{\frac{v^{2} - u^{2} }{2}}$

W = $\mathsf{\frac{1}{2}}$m $\mathsf{(v^{2} - u^{2})}}$

Here, Since workdone is equal to the Kinetic Energy of the Object,

E$\mathsf{_k}$ = $\mathsf{\frac{1}{2}}$m $\mathsf{(v^{2} - u^{2})}}$

If u = 0,

E$\mathsf{_k}$ = $\mathsf{\frac{1}{2}}$m $\mathsf{v^{2}}}$

Answer 2

hi mate your answer
Suppose a Force ‘F’ acting on a body of mass ‘m’ in state of rest changes its velocity to ‘v’ and body covers ‘s’ distance in the direction of force.

Then, the work done by the force is given by

W = F . S

= ma . S …………(1) [ F = ma ]

Now, using equation of motion, we have

v2 = u2 + 2aS

or, v2 = 0 + 2aS

as = v2/2

So, by equation (1) , we get

W = m .v2/2

so , by definition of kinetic energy of the body,

K.E. = W = 1/2 mv2