Equations of Motion
Summary
- The following equations of motion are valid only when…
- acceleration is constant
- motion is constrained to a straight line
| 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
| traditional name | equation | relationship |
|---|---|---|
| 1st equation | v = v0 + at | velocity-time |
| 2nd equation | ∆s = v0t + ½at2 | displacement-time |
| 3rd equation | v2 = v02 + 2a∆s | velocity-displacement |
| mentor 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.)