Motion, Force and Laws of Motion
Motion, force and laws of motion supplies the numerical part of the physics section: speed, acceleration, graphs and Newton's laws.
Distance, displacement, speed, velocity
Distance is a scalar; displacement is a vector and is always less than or equal to the distance. Speed = distance/time; velocity = displacement/time, with direction. The average speed of a round trip is total distance/total time, not the mean of the two speeds. Acceleration a = (v − u)/t, in m/s²; negative acceleration is retardation.
Graphs and equations of motion
On a distance–time graph the slope is speed; on a velocity–time graph the slope is acceleration and the area under the graph is distance. For uniform acceleration: v = u + at; s = ut + ½at²; v² = u² + 2as.
Newton's laws
First law: a body stays at rest or in uniform motion unless a net external force acts (inertia). Second law: F = ma; force is the rate of change of momentum. Third law: every action has an equal and opposite reaction, acting on a different body. Momentum p = mv, in kg m/s; total momentum is conserved when no external force acts.
Worked example
A car starts from rest and accelerates uniformly at 2 m/s² for 5 s. v = u + at = 0 + 2 × 5 = 10 m/s. s = ut + ½at² = 0 + ½ × 2 × 25 = 25 m. For a 1000 kg car, momentum after 5 s = 1000 × 10 = 10,000 kg m/s.
Traps
Using the average of two speeds for a two-way journey; thinking action and reaction cancel (they act on different bodies); mixing up slope and area on a velocity–time graph; using g = 10 when the question gives 9.8.