What is the dimensional consistency of s = Vot + 1/2 at2

The formula is dimensionally consistent

Explanation:

Dimensional Analysis

There are three fundamental magnitudes in Physics:

L = Length

T = Time

M = Mass

All the formulas and equations that use physical magnitudes must be consistent in their units.

For example, the formula:

Is used to calculate the distance traveled by an object, knowing its initial speed vo, acceleration a, and time t.

The units for each magnitude are:

s   = L

vo = L/T or

a   = L/T^2 or

Let's analyze the dimensions of the magnitudes in the formula (the constant 1/2 is neglected because it doesn't affect the dimensional analysis):

The first term simplifies to L because the T's simplify. The same happens with the second term, the squared T's simplify:

Thus the formula is dimensionally consistent