The Physics
Hypertextbook
Opus in profectus

# Equations of Motion

## Summary

• The following equations of motion are valid only when…
• acceleration is constant and
• motion is constrained to a straight line.
One dimensional equations of motion for constant acceleration
1st equation v = v0 + at velocity-time
2nd equation x = x0 + v0t + ½at2 displacement-time
3rd equation v2 = v02 + 2a(x − x0) velocity-displacement
merton rule  = ½(v + v0) average velocity

Where…

 x0 = initial displacement (the displacement at the beginning of some event) x = final displacement (the displacement at the end of some event) v0 = initial velocity (the velocity at the beginning of some event) v = final velocity (the velocity at the end of some event) a = acceleration t = time (the duration of the event)
• The signs on quantities should be…
• the same if they act in the same direction
• opposite if they act in opposite directions
• The choice of which direction is positive and which is negative is arbitrary.
• The laws of physics are isotropic (are not affected by your choice).
• Make your decision and stick with it. (Be consistent.)