Question

Why is velocity squared in kinetic energy and mass multiplied by 1/2?

Answer 1

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[$\frac{v^{2}-u^{2} }{2}$]
∴W = $\frac{mv^{2} }{2} - \frac{mu^{2} }{2}$

Which is nothing but change in kinetic energy.
That is how kinetic energy is derived