Forces and motion

Revision notes

Forces are vector interactions. Contact forces include friction, tension and normal contact force; non-contact forces include gravity and magnetism. Weight is W = mg and work done by a force transfers energy. Distance and speed are scalars, while displacement and velocity are vectors. Acceleration is change in velocity per unit time and resultant force is linked to mass and acceleration by F = ma. Distance-time and velocity-time graphs represent motion. A falling object in a fluid can eventually reach terminal velocity when its resultant force becomes zero. Newton's laws link resultant force and motion. Stopping distance is thinking distance plus braking distance and depends on reaction time, speed, road conditions and braking conditions. At Higher Tier, momentum is p = mv and total momentum is conserved in a closed system.

Describing motion

Speed describes how quickly distance is covered, while velocity also includes direction. Acceleration is the rate of change of velocity. A negative acceleration means acceleration acts in the chosen negative direction; it does not automatically mean the object is slowing down.

On a distance-time graph, gradient represents speed. On a velocity-time graph, gradient represents acceleration. A horizontal velocity-time line means constant velocity, not necessarily zero velocity.

Resultant force and Newton's laws

Forces are vectors, so direction matters. The resultant force is the vector sum of all forces acting on an object. If the resultant force is zero, velocity stays constant. If there is a non-zero resultant force, the object accelerates in the direction of that resultant force.

For constant mass, F = ma. Mass measures inertia; weight is the gravitational force on the mass and is given by W = mg.

Stopping and force reasoning

Stopping distance is thinking distance plus braking distance. Thinking distance is proportional to speed for a given reaction time (typically 0.2–0.9 s, longer when tired, distracted or after alcohol or drugs). Because kinetic energy depends on v², doubling the speed roughly quadruples the braking distance for the same braking force.

For uniform acceleration, v² − u² = 2as links initial velocity u, final velocity v, acceleration a and distance s; use it when time is not given. Typical speeds help with estimates: walking about 1.5 m/s, cycling about 6 m/s, a car on a main road about 13–30 m/s, sound in air about 330 m/s.

Exam technique

Draw or imagine a free-body diagram before choosing a force equation. Keep one direction positive throughout a calculation. When interpreting motion graphs, refer to gradients and graph sections rather than only describing the story in words.