Forces and Motion

What you'll learn

This revision guide covers all aspects of Forces and Motion tested in the Pearson Edexcel International IGCSE Physics specification. You'll master calculating speed, velocity and acceleration, interpreting motion graphs, applying Newton's laws, and analysing momentum and stopping distances. These concepts form the foundation for further mechanics studies and appear frequently across papers.

Key terms and definitions

Speed — the distance travelled per unit time, measured in metres per second (m/s) or kilometres per hour (km/h); speed is a scalar quantity with magnitude only

Velocity — the displacement (distance in a given direction) per unit time, measured in m/s; velocity is a vector quantity with both magnitude and direction

Acceleration — the rate of change of velocity, measured in metres per second squared (m/s²); can be positive (speeding up) or negative/deceleration (slowing down)

Momentum — the product of mass and velocity (p = mv), measured in kilogram metres per second (kg m/s); a vector quantity conserved in collisions

Resultant force — the single force that has the same effect as all the individual forces acting on an object combined using vector addition

Inertia — the tendency of an object to resist changes in its state of motion; greater mass means greater inertia

Terminal velocity — the constant maximum velocity reached by a falling object when the upward forces (air resistance and upthrust) equal the downward force (weight)

Stopping distance — the total distance a vehicle travels from when the driver perceives a hazard until the vehicle stops, equal to thinking distance plus braking distance

Core concepts

Speed, distance and time calculations

The fundamental relationship between speed, distance and time is:

speed = distance ÷ time or v = d/t

You must be able to rearrange this equation to find any variable:

• distance = speed × time (d = vt)
• time = distance ÷ speed (t = d/v)

Average speed is calculated over the entire journey: average speed = total distance travelled ÷ total time taken

For uniform (constant) speed, instantaneous speed equals average speed throughout. For non-uniform motion, instantaneous speed varies, so average speed gives an overall measure.

Velocity and acceleration

Velocity differs from speed because it includes direction. A car travelling at 20 m/s north has a different velocity from one travelling at 20 m/s south, though both have the same speed.

Acceleration measures how quickly velocity changes:

acceleration = change in velocity ÷ time taken or a = (v - u)/t

where:

• u = initial velocity (m/s)
• v = final velocity (m/s)
• t = time taken (s)
• a = acceleration (m/s²)

Key equations of motion (for uniform acceleration only):

• v = u + at
• s = (u + v)t/2
• v² = u² + 2as
• s = ut + ½at²

where s = displacement (distance in a given direction)

Deceleration is negative acceleration. If a car slows from 30 m/s to 10 m/s in 4 s: a = (10 - 30)/4 = -5 m/s²

Distance-time and velocity-time graphs

Distance-time graphs show how distance from a starting point changes over time:

• Gradient (slope) = speed
• Horizontal line = stationary (zero speed)
• Straight sloping line = constant speed
• Curved line = changing speed (accelerating or decelerating)
• Steeper gradient = higher speed

Velocity-time graphs show how velocity changes over time:

• Gradient = acceleration
• Horizontal line = constant velocity (zero acceleration)
• Straight sloping line = constant acceleration
• Area under graph = displacement
• Line sloping downward = deceleration (negative acceleration)

To calculate distance from a velocity-time graph, find the area under the line. For complex shapes, divide into triangles and rectangles, calculate each area separately, then sum them.

Newton's laws of motion

Newton's First Law (Law of Inertia): An object remains at rest or continues moving at constant velocity unless acted upon by a resultant force.

This explains why:

• Passengers lurch forward when a bus brakes suddenly (they continue at the original velocity)
• Seat belts and headrests are essential safety features
• Objects in space continue moving indefinitely without friction

Newton's Second Law: The acceleration of an object is proportional to the resultant force acting on it and inversely proportional to its mass.

F = ma or resultant force = mass × acceleration

where:

• F = resultant force (N)
• m = mass (kg)
• a = acceleration (m/s²)

This law shows:

• Larger force → greater acceleration
• Larger mass → smaller acceleration (for same force)
• Same force on different masses produces different accelerations

Newton's Third Law: When object A exerts a force on object B, object B exerts an equal and opposite force on object A.

Key points:

• The forces act on different objects (action-reaction pairs)
• The forces are equal in magnitude
• The forces are opposite in direction
• The forces are the same type (both gravitational, both contact forces, etc.)

Examples: rocket thrust and exhaust gases; book on table (weight down, normal reaction up); Earth pulls Moon, Moon pulls Earth.

Momentum and its conservation

Momentum (p) = mass (m) × velocity (v)

p = mv (measured in kg m/s)

The principle of conservation of momentum states: In a closed system (no external forces), the total momentum before a collision equals the total momentum after the collision.

For two objects colliding: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

where u represents initial velocities and v represents final velocities.

Types of collision:

• Elastic collision — objects bounce apart; both momentum and kinetic energy conserved (rare in real life)
• Inelastic collision — objects may deform or stick together; momentum conserved but kinetic energy converted to heat/sound/deformation

Applications include:

• Car safety design (crumple zones increase collision time, reducing force)
• Understanding explosions (total momentum before = 0, so momentum after must sum to zero)
• Sports analysis (bat hitting ball, snooker ball collisions)

Force, mass and weight

Mass is the amount of matter in an object, measured in kilograms (kg). Mass is a scalar quantity and remains constant regardless of location.

Weight is the gravitational force acting on an object's mass, measured in newtons (N). Weight is a vector quantity acting downward toward Earth's centre.

weight = mass × gravitational field strength or W = mg

where:

• W = weight (N)
• m = mass (kg)
• g = gravitational field strength (N/kg)

On Earth's surface, g ≈ 10 N/kg (or 9.8 N/kg for more precise calculations). On the Moon, g ≈ 1.6 N/kg.

A 60 kg astronaut has:

• Mass = 60 kg everywhere
• Weight on Earth = 60 × 10 = 600 N
• Weight on Moon = 60 × 1.6 = 96 N

Stopping distances

Stopping distance = thinking distance + braking distance

Thinking distance is how far the vehicle travels during the driver's reaction time (typically 0.6–0.9 seconds). It depends on:

• Speed (faster = greater thinking distance; direct proportion)
• Driver's reaction time (tiredness, alcohol, drugs, distractions increase it)

Braking distance is how far the vehicle travels after brakes are applied until it stops. It depends on:

• Speed (doubling speed quadruples braking distance; square relationship)
• Vehicle condition (worn brakes/tyres increase it)
• Road conditions (wet, icy roads increase it)
• Vehicle mass (heavier vehicle = longer braking distance)

Typical UK Highway Code values (approximations):

• At 30 mph (13 m/s): thinking 9 m + braking 14 m = 23 m total
• At 60 mph (27 m/s): thinking 18 m + braking 55 m = 73 m total

Worked examples

Example 1: Calculating acceleration

Question: A car accelerates from rest to 25 m/s in 8.0 seconds. Calculate the acceleration of the car. (2 marks)

Solution:

• Initial velocity, u = 0 m/s (starts from rest)
• Final velocity, v = 25 m/s
• Time, t = 8.0 s
• Using a = (v - u)/t (1 mark for correct formula or working)
• a = (25 - 0)/8.0 = 3.125 m/s²
• a = 3.1 m/s² (1 mark for correct answer with unit)

Example 2: Using a velocity-time graph

Question: The graph shows the motion of a cyclist over 30 seconds. The cyclist accelerates uniformly from rest to 8 m/s in the first 10 seconds, travels at constant velocity for 10 seconds, then decelerates uniformly to rest over the final 10 seconds.

(a) Calculate the acceleration in the first 10 seconds. (2 marks) (b) Calculate the total distance travelled. (3 marks)

Solution:

(a)

• Acceleration = gradient = change in velocity ÷ time (1 mark)
• a = (8 - 0) ÷ 10 = 0.8 m/s² (1 mark)

(b)

• Distance = area under velocity-time graph (1 mark)
• Area of triangle 1 = ½ × 10 × 8 = 40 m
• Area of rectangle = 10 × 8 = 80 m
• Area of triangle 2 = ½ × 10 × 8 = 40 m
• Total distance = 40 + 80 + 40 = 160 m (1 mark for method, 1 mark for answer)

Example 3: Conservation of momentum

Question: A railway truck of mass 8000 kg moving at 3.0 m/s collides with a stationary truck of mass 4000 kg. The trucks couple together. Calculate their velocity immediately after collision. (3 marks)

Solution:

• Total momentum before = total momentum after (1 mark for principle)
• Before: p = (8000 × 3.0) + (4000 × 0) = 24 000 kg m/s
• After: p = (8000 + 4000) × v = 12 000v
• 24 000 = 12 000v (1 mark for correct working)
• v = 24 000 ÷ 12 000 = 2.0 m/s (1 mark for answer with unit)

Common mistakes and how to avoid them

• Confusing speed and velocity — Remember velocity includes direction. Two objects with the same speed but different directions have different velocities. In calculations, if direction changes, velocity changes even if speed stays constant.

• Using the wrong units — Always convert to SI base units: km/h to m/s (divide by 3.6), g to kg (divide by 1000), cm to m (divide by 100). Check units match in formulas: if mass is in kg and acceleration in m/s², force will be in N.

• Mixing up distance-time and velocity-time graphs — The gradient of a distance-time graph gives speed, not acceleration. The gradient of a velocity-time graph gives acceleration. Distance comes from the area under a velocity-time graph, not a distance-time graph.

• Applying equations to non-uniform acceleration — The equations v = u + at, s = ut + ½at², etc., only work for constant (uniform) acceleration. Don't use them when acceleration varies.

• Forgetting Newton's Third Law force pairs act on different objects — The weight of a book and the normal reaction from a table are NOT Newton's Third Law pairs because both act on the book. The pairs are: (1) Earth pulls book down / book pulls Earth up; (2) book pushes table down / table pushes book up.

• Assuming thinking distance increases with speed squared — Thinking distance is directly proportional to speed (double speed → double thinking distance), but braking distance increases with speed squared (double speed → quadruple braking distance).

Exam technique for "Forces and Motion"

• Command word 'calculate' requires numerical working — Show the formula, substitute values with units, then give the answer with the correct unit. Marks are awarded for method even if the final answer is wrong, so always show working clearly.

• For 'explain' questions, link cause and effect — Don't just state facts. Use connecting words: "because," "therefore," "so," "this causes." Example: "The resultant force is zero, so (by Newton's First Law) the car moves at constant velocity."

• Graph questions often carry 3–4 marks — Read values carefully from axes. For gradient calculations, choose points far apart and show Δy/Δx clearly. For area calculations under velocity-time graphs, split complex shapes into triangles and rectangles, calculate each separately, then sum.

• Check your answer makes physical sense — If you calculate a bicycle's acceleration as 500 m/s², you've made an error. If stopping distance decreases when speed increases, reconsider your working. Use everyday experience to spot impossible answers.

Quick revision summary

Forces and Motion links distance, speed, velocity, acceleration, force and momentum through mathematical relationships. Master the key equations: v = d/t, a = (v - u)/t, F = ma, p = mv. Interpret distance-time graphs (gradient = speed) and velocity-time graphs (gradient = acceleration, area = distance). Apply Newton's three laws, especially F = ma and conservation of momentum in collisions. Understand stopping distance components and their dependence on speed. Always show working, use correct units, and check answers are physically reasonable.