Forces and motion

Revision notes

A force is an interaction that can change an object's velocity or shape. Forces are vectors, so direction matters. The resultant force is the vector sum of all forces. If the resultant force is zero, an object remains at rest or continues at constant velocity.

Acceleration is change in velocity per unit time: a = \(\dfrac{\Delta v}{t}\). For constant mass, resultant force and acceleration are linked by F = ma. Momentum is p = mv and is conserved in a closed system. Stopping distance is thinking distance plus braking distance; speed, reaction time, road conditions, tyres and brakes all matter. Terminal velocity occurs when resistive forces grow until they balance the driving force, making resultant force and acceleration zero.

Describing motion

Distance is a scalar; displacement is a vector. Speed is distance travelled per unit time, while velocity includes direction. Acceleration is the rate of change of velocity, a = \(\dfrac{\Delta v}{t}\). A negative acceleration does not automatically mean an object is slowing down: it means the acceleration is in the chosen negative direction. Whether speed increases or decreases depends on the directions of velocity and acceleration.

On a distance-time graph, gradient represents speed. On a velocity-time graph, gradient represents acceleration and the area between the graph and the time axis represents displacement. A horizontal velocity-time line means constant velocity, not that the object is stationary. Curved sections require interpretation: a changing gradient means changing acceleration. To find the speed at one instant on a curved distance-time graph, draw a tangent and find its gradient.

For uniform acceleration, v² − u² = 2as links initial velocity u, final velocity v, acceleration a and distance s. It is useful when time is not given, for example to find how far a car travels while braking from a known speed.

Forces and Newton's laws

A force can change motion, shape or both. The resultant force is the vector sum of all forces. Newton's first law: if the resultant force is zero, velocity is constant; this includes remaining stationary. Newton's second law: if there is a non-zero resultant force, the object accelerates according to F = ma, in the direction of the resultant force. Mass measures inertia, while weight is the gravitational force W = mg. Mass is measured in kilograms and stays the same when location changes; weight is measured in newtons and depends on gravitational field strength.

Newton's third law concerns interaction pairs. If object A exerts a force on object B, B exerts an equal-magnitude, opposite-direction force on A. These forces act on different objects, so they do not cancel each other on a free-body diagram of one object.

Momentum, collisions and stopping

Momentum p = mv is a vector. In a closed system, total momentum before an interaction equals total momentum after it. Kinetic energy, however, need not be conserved in a collision because energy can be transferred to thermal stores, sound and deformation. In explosion-style problems, an initially stationary system has total momentum zero, so the momenta after separation are equal in magnitude and opposite in direction.

Stopping distance is thinking distance plus braking distance. Thinking distance increases with reaction time and speed; reaction time can be affected by tiredness, distraction, alcohol or drugs. Braking distance depends on speed, mass, tyre and road condition, brake condition and gradient. Because kinetic energy depends on v², doubling the speed roughly quadruples the braking distance for the same braking force (work done by the brakes, Fd, must equal the kinetic energy removed).

Typical values are useful for 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. A typical reaction time is 0.2–0.9 s, longer when a driver is tired, distracted or has taken alcohol or drugs.

Exam technique

Draw a free-body diagram before using F = ma. Decide on a positive direction and keep signs consistent. On graph questions, quote evidence from the graph rather than only describing the story. For multi-step problems, calculate intermediate quantities clearly instead of trying to combine everything mentally.

Conservation of momentum

In a closed system (no external forces), the total momentum before an event equals the total momentum after it. This applies to collisions and explosions.

Worked example: a 2.0 kg trolley moving at 3.0 m/s collides with a stationary 1.0 kg trolley and they stick together. Momentum before = 2.0 × 3.0 = 6.0 kg m/s. After, (2.0 + 1.0) × v = 6.0, so v = 2.0 m/s.

Separate physics: force equals the rate of change of momentum: F = Δ(mv) ÷ t. Increasing the time taken for a change in momentum reduces the force, which is why seat belts, air bags, crumple zones and cycle helmets reduce injuries.

Newton's third law and free-body diagrams

When two objects interact, they exert equal and opposite forces on each other (Newton's third law). The two forces act on different objects and are the same type of force.

A free-body diagram shows all the forces acting on one object as arrows, with length showing size and direction showing direction. Forces at an angle can be combined with a scale drawing to find the resultant, or a single force can be resolved into two perpendicular components.