Kinematics
What this domain tests
Kinematics tests motion without forces: displacement versus distance, velocity versus speed, acceleration, graphs, relative motion and projectile motion. Expect numerical questions with uniform acceleration and interpretation of x-t and v-t graphs.
Core rules
- For constant acceleration: v = u + at, s = ut + 1/2 at^2, v^2 = u^2 + 2as. Use sign convention consistently.
- Slope of x-t graph = velocity; slope of v-t graph = acceleration; area under v-t = displacement.
- Relative velocity: v_AB = v_A - v_B in one dimension; in two dimensions subtract vectors.
- Projectile: horizontal velocity constant; vertical acceleration g. Time of flight T = 2u sinθ/g; range R = u^2 sin2θ/g; maximum height H = u^2 sin^2θ/(2g).
- At maximum height vertical velocity is zero, but horizontal velocity is not.
Worked example
A ball is projected at 20 m/s at 30° to the horizontal. Take g = 10 m/s². Find time of flight and range. u_x = 20 cos30° = 17.3 m/s; u_y = 20 sin30° = 10 m/s. T = 2u_y/g = 2 s. R = u_x T = 17.3 × 2 = 34.6 m. Using R = u² sin60°/g gives 400 × 0.866/10 = 34.6 m, confirming the result.
Traps
Do not use g = 9.8 m/s² when the paper specifies 10. Do not add horizontal and vertical components as scalars. In v-t graphs, negative area means displacement in the opposite direction. Average speed uses total distance, not displacement.