Motion and Relativity
Core concepts
Motion in SACE Stage 2 rests on distinguishing scalars (distance, speed, mass) from vectors (displacement, velocity, acceleration). Velocity is the rate of change of displacement, so a change of direction is an acceleration even at constant speed. Use the constant-acceleration equations only when acceleration is uniform, and always define a positive direction before substituting signs.
Projectile motion separates into independent horizontal and vertical components: horizontal velocity stays constant (ignoring air resistance) while vertical motion accelerates at g downward. Circular motion introduces centripetal acceleration a = v²/r directed toward the centre; the centripetal force is a net force, never an extra force to add to a free-body diagram.
Momentum p = mv is conserved in collisions and explosions when external forces are negligible; kinetic energy is conserved only in elastic collisions. Impulse equals change in momentum, so a longer contact time reduces the average force.
Relativity follows from the invariance of the speed of light. Time dilation t = t₀/√(1 − v²/c²) and length contraction apply to measurements made in different inertial frames. Relativistic momentum and energy (E = mc², total energy E = γmc²) matter when v approaches c.
Traps
Mixing up distance and displacement; forgetting that at maximum height vertical velocity is zero but horizontal velocity is not; treating centripetal force as an additional force; applying conservation of kinetic energy to inelastic collisions; using the rest-time symbol in the wrong frame; assuming relativistic effects are noticeable at everyday speeds.
Worked example
A ball is thrown horizontally at 15 m/s from a 20 m cliff. Time to fall: t = √(2h/g) = √(40/9.8) ≈ 2.02 s. Horizontal range: x = vt = 15 × 2.02 ≈ 30 m. Rule of thumb: split projectile problems into two independent one-dimensional problems linked only by time.