§ 2.1 Equations of motion
Key ideas
- Displacement is the straight-line distance from start to finish (a vector); velocity is the rate of change of displacement; acceleration is the rate of change of velocity.
- Graphs: the gradient of a displacement-time graph is velocity; the gradient of a velocity-time graph is acceleration; the area under a velocity-time graph is displacement.
- The SUVAT equations apply only while acceleration is constant; each one omits exactly one of the five quantities.
- Free fall: g = 9.81 m s⁻². Measure it by timing a falling object: plot s against t², and the gradient is ½g.
- Projectiles: treat the horizontal motion (uniform velocity, vx = u cos θ) and the vertical motion (uniform acceleration g downward) as completely independent.
Equations
v = u + atno s: final velocity from timem s⁻¹
s = ½(u + v)tno a: displacement from average velocitym
s = ut + ½at²no v: displacement from timem
v² = u² + 2asno t: final velocity from displacementm² s⁻²
Fig. 1 · The velocity-time graph holds everything: read u from the intercept, a from the gradient, and s from the area under the line.
Fig. 2 · A projectile: gravity acts only vertically, so vx never changes while vy grows; the two motions share nothing but the time.
Watch out: pick one direction as positive and keep it. Throwing upwards with u = +20 m s⁻¹ means a = −9.81 m s⁻²; mixing signs mid-question is the most common SUVAT error.