Acceleration magnitude is measured in units of distance per time interval squared.
Velocity magnitude is measured in units of distance per time interval.
Spacial displacement is measured in units of distance.
If you multiply acceleration by a time interval, one of the time interval factors in the acceleration dimension denominator is canceled and you get a velocity magnitude. So the first equation is dimensionally correct because you are adding a velocity to a velocity.
If you multiply velocity by a time interval, you cancel the time interval in the velocity dimension denominator and you get a spacial displacement and if you multiply acceleration by a time interval squared you cancel the squared time interval in the acceleration dimension denominator and you get a spacial displacement. So the second equation is dimensionally correct because you are adding a distance to a distance.
John
My calculator said it, I believe it, that settles it
