Motion
Motion tests how position, distance, displacement, speed, velocity and acceleration are described, including motion graphs and uniform circular motion. Numerical questions usually need the three equations of motion for constant acceleration.
Core ideas
- Distance is the total path length (scalar); displacement is the straight-line change in position with direction (vector).
- Speed = distance/time; velocity = displacement/time. Average speed uses total distance and total time.
- Acceleration a = (v - u)/t. Negative acceleration means the velocity decreases along the chosen positive direction.
- For constant acceleration: v = u + at; s = ut + (1/2)at^2; v^2 = u^2 + 2as; also s = (u + v)t/2.
- On a distance-time graph, slope gives speed. On a velocity-time graph, slope gives acceleration and area under the line gives displacement.
- Uniform circular motion has constant speed but changing velocity because direction changes.
Worked example
A car speeds up from 10 m/s to 30 m/s in 5 s. Find acceleration and distance. a = (30 - 10)/5 = 4 m/s^2. Using s = (u + v)t/2 = (10 + 30)(5)/2 = 100 m. Check with s = ut + (1/2)at^2 = 10(5) + 0.5(4)(25) = 50 + 50 = 100 m. Reasoning: the two results agree because acceleration is constant.
Traps that cost marks
A round trip can have zero displacement but non-zero distance. Do not confuse speed and velocity. In graph questions, read the axis labels before using slope or area. Convert km/h to m/s by multiplying by 5/18.