Physics
Uniformly Accelerated Motion
Basic Formulas
In uniformly accelerated motion, the velocity changes by the same amount over equal time intervals, that is, a = const.
- Velocity: v = v₀ + a·t.
- Distance: s = v₀t + at²/2.
- Time-independent formula: v² − v₀² = 2as.
- Average velocity: v_avg = (v₀ + v)/2.
Special Cases
| Case | Formulas |
|---|---|
| No initial velocity (v₀ = 0) | v = at, s = at²/2 |
| Braking (deceleration) | a is negative, v decreases |
- In braking, a is negative: if v₀ = 20 m/s and a = −4 m/s², the distance until stopping is s = 400/(2·4) = 50 m.
- At the moment of stopping, the final velocity is v = 0.
Examples
- v₀ = 0, a = 3 m/s², t = 4 s: v = 3·4 = 12 m/s, s = 3·16/2 = 24 m.
- Distance depends on the square of time: if the time increases 2 times, the distance increases 4 times (when v₀ = 0).
- What is given: v₀, a, t or s
- To find the velocity, use v = v₀ + at
- If time is not given, use v² − v₀² = 2as