Question

How to check the correctness of v2-u2 = 2as? In dimensional analysis

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]

L.H.S=v²-u²=[LT⁻¹]²=[L²T⁻²]

Therefore  L.H.S=R.H.S

Hence we can say equation is correct

Answer 2

v= final velocity = [LT-¹]

u= initial velocity=[LT-¹]

a= acceleration =[LT-²]

s= distance= [L]

v²=u²+ 2as

=>v²-u²=2as

[LT-¹]²-[LT-¹]²=2[LT-²][L]

[L²T-²][L²T-²]=2[L²T-²]

2[L²T-²]=2[L²T-²]

2 is dimensionless

hence proved