Remember the definition of work done.
Work done is force(F) times displacement(x)
∴ W = F.Δx
According to Newton's 2nd law of motion,
F = ma
∴ W = ma.Δx ---- (i)
Using the kinematical equation v²-u² = 2ax,
aΔx = (v²-u²)/2
Plug this value in (i),
∴W = m[[tex] \frac{v^{2}-u^{2} }{2} [/tex]]
∴W = [tex] \frac{mv^{2} }{2} - \frac{mu^{2} }{2} [/tex]
Which is nothing but change in kinetic energy.
That is how kinetic energy is derived
