Question

link to chapter 1.4. (problem 1.4.51 - 53)
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: Substitute dimensions

Substitute $[s] = L$, $[v]=LT^{-1}$, $[a]=LT^{-2}$ into the left - hand side of the equation $v^{2}=2as$.
$[v^{2}]=[v]\times[v]=(LT^{-1})\times(LT^{-1}) = L^{2}T^{-2}$

Step2: Substitute dimensions into right - hand side

Substitute into the right - hand side. $[2as]=[a]\times[s]=(LT^{-2})\times L = L^{2}T^{-2}$

Step3: Compare dimensions

Since the dimension of the left - hand side $L^{2}T^{-2}$ is equal to the dimension of the right - hand side $L^{2}T^{-2}$, the equation is dimensionally consistent.

Answer:

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