There are usually said to be six “suvat” equations of motion, but they’re all derived from the two previous velocity and acceleration equations. The five measures, with their respective SI units are shown below:
- s – displacement (m)
- u – (sometimes vi) initial velocity (m·s-1)
- v – final velocity (m·s-1)
- a – acceleration (m·s-2)
- t – time (s)
Equations #1 and 2
Since change in velocity is calculated by subtracting final velocity from initial velocity, the acceleration equation can be re-written as:
Or re-arranged to:
Equation #3
Like the previous equations, equation #3 is simply a slightly expanded version of the original velocity equation. Average velocity (the sum of initial and final velocity, then divided by 2) is substituted in, and then rearranged:
Equations #4 and 5
To obtain the fourth equation, #2 is substituted into #3, then simplified and re-arranged:
An equation of similar form allows the use of final velocity instead of initial velocity:
Equation #6
Finally equation #2 can be substituted into #3 to give:
