Answer:
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:
[tex]\displaystyle s=v_ot+\frac{1}{2}at^2[/tex]
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 [tex]LT^{-1}[/tex]
a = L/T^2 or [tex]LT^{-2}[/tex]
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):
[tex]\displaystyle L=L/T*T+L/T^2*T^2[/tex]
The first term simplifies to L because the T's simplify. The same happens with the second term, the squared T's simplify:
[tex]\displaystyle L=L+L[/tex]
Thus the formula is dimensionally consistent
