Question

How to prove dimensions for the equation v²=u²+2ax

Answer 1

We can check the correctness of equation by Dimensional Analysis.
Equation: V²=U²-2as

where V=u=velocities = Dimension=LT⁻¹

a= acceleration=ΔV/T=LT⁻¹/T=LT⁻²

S=Distance=L

R.H.S=2as=2x[LT⁻²]x[L]=[L²T⁻²]

Dimension of L.H.S=[v²] =[u²] =[LT⁻¹]²=[L²T⁻²]

Therefore L.H.S=R.H.S

Hence we can say equation is correct