Question

Easy derivation of kinetic energy

Answer 1

Expression for Kinetic energy(Ek)-

Consider an object with mass m, moving with initial velocity u. Let a force F, act on it causing a displacement s, along the direction of force and accelaration.
Let the object attain final velocity v.
We know
F = m x a ------------------------ 1
By position velocity relation we have,

​​​​​v^2 = u^2 + 2as or
s = v^2 -u^2 / 2a ----------------------------- 2
The work done by the force
W = F x s -------------------------------------- 3
Substituting 1 and 2 in 3
W
= (m x a) x (v^2 - u^2/2a)
= m/2 (v^2 - u^2)
= 1/2 mv^2 - 1/2 mu^2 -------------------- 4
For an object to be at rest in the beggining, u = 0 Therefore, W = 1/2 mv^2
W = Ek ( Ek = kinetic energy)
Therefore, Ek = 1/2 mv^2