Understanding Dimensional Analysis in Basic Linear Motion Formulas

[lozzajp]

One thing I enjoy as a new physics student is using formulas. I have been playing with the fundamental formulas in terms of units rather than their names.

That is instead of a=v/t
m/s/s=(m/s)/s

or v=at
m/s=(m/s/s) x s
m/s=m/s

Simple maths yea, but when I am getting to the bigger formulas I am having trouble, perhaps they just don't work the way i am thinking but if someone could enlighten me that would be great..

S=(1/2)at^2
m=(1/2)x(m/s^2)x(s^2)
m=(1/2)x(m)

why do i get m = half m?

v^2 = 2as
m^2/s^2 = 2(m/s/s) x m
m^2/s^2 = 2 x m^2/s^2
m/s = 2 x m/s

again, there is a x2 factor there.

am i just thinking about this too much?

 

[HallsofIvy]

If you are only looking at the units you are throwing away any "dimensionless" constants in the formulas. From that point of view, there is not difference between "m" and "m/2"- both have dimensions of "meters" which is all you are looking at.