Kinematics and Dynamics: Motion
This domain tests how well you describe motion in one dimension and connect words, graphs and equations. Expect questions on scalars and vectors, distance and displacement, speed and velocity, acceleration, motion graphs, and uniformly accelerated motion including free fall.
Core rules and concepts
- Distance is a scalar path length; displacement is a vector change of position. Speed is scalar; velocity is speed in a stated direction.
- Acceleration a = (v − u)/t. The equations for constant acceleration are v = u + at, s = ut + ½at² and v² = u² + 2as.
- On a displacement–time graph, the gradient is velocity. On a velocity–time graph, the gradient is acceleration and the area under the line is displacement.
- Free fall: near Earth, g is about 9.8 m/s² (often 10 m/s² in questions). Upward motion is positive if you choose that direction, so a falling object has negative acceleration.
- Terminal velocity occurs when air resistance equals weight; resultant force is zero and acceleration becomes zero.
Worked example
A car starts from rest and accelerates at 2.0 m/s² for 6.0 s. It then travels at constant velocity for 4.0 s. Find the total distance. First phase: v = u + at = 0 + 2.0 × 6.0 = 12 m/s. Distance s₁ = ut + ½at² = 0 + ½ × 2.0 × 6.0² = 36 m. Second phase: constant velocity 12 m/s for 4.0 s, so s₂ = vt = 12 × 4.0 = 48 m. Total distance = 36 + 48 = 84 m. Reasoning: split the motion into phases with different acceleration; do not use one equation for the whole trip.
Traps that cost marks
- Treating speed and velocity, or distance and displacement, as interchangeable.
- Reading the area under a displacement–time graph instead of its gradient.
- Forgetting that the area under a velocity–time graph is displacement, not acceleration.
- Using average speed for an accelerating object as if speed were constant.
- Losing the sign of g when an object is thrown upward.