Question

consider the physical quantities with dimensions: s=l, v=lt^(-1), a=lt^(-2), and t=t. determine whether each of the equations below are dimensionally consistent.
(a) v^2 = 2as

Explanation:

Step1: Find dimensions of left - hand side

The dimension of $v$ is $[v]=LT^{-1}$. So, for $v^{2}$, the dimension is $[v^{2}]=(LT^{-1})^{2}=L^{2}T^{-2}$.

Step2: Find dimensions of right - hand side

The dimension of $a$ is $[a]=LT^{-2}$ and the dimension of $s$ is $[s]=L$. Then the dimension of $2as$ (the factor 2 is dimensionless) is $[2as]=[a][s]=LT^{-2}\times L = L^{2}T^{-2}$.

Step3: Compare dimensions

Since the dimension of the left - hand side $[v^{2}]=L^{2}T^{-2}$ and the dimension of the right - hand side $[2as]=L^{2}T^{-2}$, the equation is dimensionally consistent.

Answer:

The equation $v^{2}=2as$ is dimensionally consistent.