Question

a body of mass m is at rest a force f is applied on it which produces uniform acc . A and displaces through a distance S if v be the velocity find the ecpression of kinetic energy​

Answer 1

Answer :-

Let us first know, what is kinetic energy -

Kinetic energy :- Energy possessed by virtue of motion of an object is called kinetic energy.

Mathematical expression for kinetic energy -

Given that,

• Initial velocity = 0
• Force = F
• Acceleration = a
• Displacement = s
• Final Velocity = v

By using 3rd equation of motion -

➩ $\sf v^2 = u^2 + 2as$

➩ $\sf v^2 = 2as$

➩ $\sf a = \frac{v^2}{2s}$

We know that,

Force = ma

Also,

Work done = Force × Displacement

= mas

Substituting the value we obtained -

Work done = mas

$\sf = m \times \frac{v^2}{2\cancel{s}} \times \cancel{s}$

$\sf = \frac{mv^2}{2}$

So, by definition of kinetic energy

$\boxed{\sf K.E. = \frac{1}{2} mv^2}$