1.1 — Scalars and vectors
A scalar quantity has magnitude only. A vector quantity has both magnitude and direction.
| Scalars | Vectors |
|---|
| Distance, speed, mass, time, energy, temperature | Displacement, velocity, acceleration, force, momentum, weight |
Displacement = distance in a specified direction. Velocity = speed in a specified direction.
1.2 — Speed, velocity and acceleration
Distance–time graphs: gradient = speed. Flat line = stationary. Steeper gradient = faster speed. Curve = changing speed (acceleration).
Velocity–time graphs: gradient = acceleration. Area under graph = distance travelled. Horizontal line = constant velocity. Negative gradient = deceleration.
Acceleration due to gravity near Earth's surface: g ≈ 10 m/s² (9.8 m/s² in calculations where specified).
1.3 — Equations of motion (uniform acceleration)
These equations only apply when acceleration is constant (uniform). Always define u, v, a, s, t before substituting.
1.4 — Forces
A force is a push or pull measured in newtons (N). Forces can be contact (friction, tension, normal reaction, air resistance) or non-contact (gravity, magnetic, electrostatic).
The resultant force is the single force that has the same effect as all forces acting on an object. Found by adding forces as vectors (consider direction).
Free body diagrams show all forces acting on one object as arrows (length = magnitude, direction = direction of force).
1.5 — Newton's three laws
1st Law: An object remains at rest or moves with constant velocity unless acted upon by a resultant force. (Balanced forces → no acceleration.)
2nd Law: The resultant force on an object equals its mass times its acceleration: F = ma. Greater force or smaller mass → greater acceleration.
3rd Law: When object A exerts a force on object B, object B exerts an equal and opposite force on object A. The forces act on different objects, are equal in magnitude, opposite in direction, and of the same type.
Higher: identifying Newton's 3rd law pairs — e.g. Earth pulls person down (gravity); person pulls Earth up (gravity). Not the same as balanced forces on one object.
1.6 — Stopping distance
Thinking distance = speed × reaction time. Affected by: tiredness, alcohol, drugs, distractions, speed.
Braking distance = distance travelled while brakes applied. Affected by: speed (proportional to v²), road conditions (ice, wet), tyre condition, vehicle mass, brake condition.
Doubling speed doubles thinking distance but quadruples braking distance (∝ v²). This is why speed limits matter disproportionately.
1.7 — Terminal velocity and falling
A falling object accelerates due to gravity (weight downward). As speed increases, air resistance increases. When air resistance = weight, resultant force = 0 → constant velocity = terminal velocity.
On a velocity–time graph: curve steepens initially (large resultant force), then flattens to a horizontal line at terminal velocity.
A parachute dramatically increases surface area → greater air resistance at lower speed → new, lower terminal velocity.
1.8 — Momentum and impulse
Conservation of momentum: In a closed system (no external forces), total momentum before = total momentum after a collision or explosion.
Safety features (crumple zones, airbags, helmets) increase the time of impact → for same Δp, force is reduced: F = Δp/t. Longer time → smaller force on passenger.
1.9 — Work, energy and power
Conservation of energy: Energy cannot be created or destroyed, only transferred. When friction is absent, KE gained = GPE lost (e.g. falling object).
Work done against friction is transferred to thermal (heat) energy — this is why brakes get hot when a vehicle slows down.