Kinematics
Core ideas
Kinematics describes motion without asking what causes it. A candidate must be fluent in the distinction between scalars (distance, speed) and vectors (displacement, velocity, acceleration), and must be able to move between position, velocity, and acceleration graphs. Slope of a position-time graph is velocity; slope of a velocity-time graph is acceleration; area under a velocity-time graph is displacement; area under an acceleration-time graph is change in velocity.
For constant acceleration, the standard toolkit is v = v₀ + at, Δx = v₀t + ½at², v² = v₀² + 2aΔx, and Δx = ½(v₀ + v)t. Projectile motion separates into independent horizontal (constant velocity) and vertical (constant acceleration g) components; time is the shared variable that links them.
Traps
- Using distance where displacement is required (sign errors in Δx).
- Assuming a = 0 at the top of a projectile's path - vertical acceleration is always g, even at the apex.
- Forgetting that a falling object and a horizontally launched object hit the ground at the same time.
- Treating average speed as the magnitude of average velocity.
Rule of thumb
When a problem gives three of the five quantities (v₀, v, a, t, Δx), pick the equation missing the fourth. For graphs, always ask "slope or area?" before computing.
Worked example
A ball is dropped from rest and falls 20 m. Using v² = v₀² + 2aΔx with a = 10 m/s² downward: v² = 0 + 2(10)(20) = 400, so v = 20 m/s downward. The time is t = v/a = 2 s.