Kinematics
What this domain tests
Kinematics tests motion in one and two dimensions: displacement versus distance, velocity–time and position–time graphs, equations of uniformly accelerated motion, projectile motion, relative velocity and uniform circular motion.
Core rules
- For constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.
- Projectile on level ground: time of flight T = 2u sinθ/g, maximum height H = u² sin²θ/(2g), range R = u² sin2θ/g.
- Relative velocity: v_AB = v_A − v_B.
- Uniform circular motion: speed is constant but velocity changes; centripetal acceleration a = v²/r directed towards the centre.
- The slope of a position–time graph is velocity; the slope of a velocity–time graph is acceleration; area under a velocity–time graph is displacement.
Worked example
A ball is projected at 20 m/s at 30° to the horizontal. Take g = 10 m/s². T = 2 × 20 × sin30°/10 = 2 s. H = (20² × sin²30°)/(2 × 10) = (400 × 0.25)/20 = 5 m. R = (20² × sin60°)/10 = (400 × 0.866)/10 ≈ 34.6 m. The vertical and horizontal motions are independent, so the horizontal velocity remains 20 cos30° ≈ 17.3 m/s throughout.
Traps
Using the range formula for a projectile launched from a height or at a downward angle; mixing g = 9.8 and g = 10 within one problem; dropping the sign of acceleration when gravity opposes motion; confusing average speed with the magnitude of average velocity; reading a graph's value where its slope is required.