The Physics
Hypertextbook
Opus in profectus

# Equations of Motion

## Summary

• The following equations of motion are valid only when…
• acceleration is constant
• motion is constrained to a straight line
The equations of motion
traditional name equation relationship
1st equation v = v0 + at velocity-time
2nd equation s = s0 + v0t + ½at2 position-time
3rd equation v2 = v02 + 2a(s − s0) velocity-position
merton rule v = ½(v + v0) average velocity

where…

 s0 = initial position (the position at the beginning of some event) s = final position (the position 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)

Alternatively

Variation on the equations of motion
traditional name equation relationship
1st equation v = v0 + at velocity-time
2nd equation s = v0t + ½at2 displacement-time
3rd equation v2 = v02 + 2as velocity-displacement
merton rule v = ½(v + v0) average velocity

where…

 ∆s = displacement (change in position) v0 = initial velocity v = final velocity a = acceleration t = time
• The signs on the spatial quantities should be…
• the same if they point in the same direction
• opposite if they point 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.)