Question

Show whether the following question is dimensionally correct

v^2=CY+2as

where v=acceleration,a=acceleration,t=time,s=distance

Answer 1

If v is velocity,

a=acceleration,

t=time,

s=distance,

then, for the right part, we have

$$[a][s]\equiv[L^1T^{-2}][L^2]=[L^2T^{-2}]=[L^1T^{-1}]^2.$$

For the left part, we have

$$[v]^2\equiv[L^1T^{-1}]^2.$$

Therefore, the expression is dimensionally correct.