What you'll learn
This topic forms the foundation of CIE IGCSE Physics Paper 1 (Core) and Paper 2 (Extended), typically accounting for 15-20% of examination marks. You will master calculations involving speed, velocity and acceleration, interpret motion graphs, apply Newton's laws to real situations, and analyse forces acting on objects. Understanding these principles is essential for tackling numerical problems and structured questions worth 4-6 marks.
Key terms and definitions
Speed — the distance travelled per unit time, a scalar quantity measured in m/s or km/h.
Velocity — the displacement per unit time in a specified direction, a vector quantity measured in m/s.
Acceleration — the rate of change of velocity, measured in m/s². A negative acceleration represents deceleration or retardation.
Displacement — the distance measured in a straight line from the starting point in a specified direction, a vector quantity.
Newton (N) — the SI unit of force, defined as the force required to give a mass of 1 kg an acceleration of 1 m/s².
Resultant force — the single force that has the same effect as all the forces acting on an object combined.
Inertia — the tendency of an object to remain at rest or continue moving at constant velocity unless acted upon by a resultant force.
Momentum — the product of mass and velocity (p = mv), measured in kg m/s, a vector quantity.
Core concepts
Calculating speed, velocity and acceleration
The fundamental equation for average speed appears in every CIE IGCSE Physics examination:
speed = distance / time or v = s / t
For Extended tier, you must distinguish between speed and velocity. Velocity includes direction, so an object moving in a circle at constant speed has changing velocity because its direction continuously changes.
Acceleration measures how quickly velocity changes:
acceleration = change in velocity / time taken or a = (v - u) / t
where u = initial velocity and v = final velocity.
The equation can be rearranged to find final velocity:
v = u + at
For Extended tier candidates, you must know:
v² = u² + 2as
where s = distance travelled during acceleration.
Typical examination questions provide three values and require calculation of the fourth. Always write the equation first, substitute values with units, then calculate.
Distance-time and speed-time graphs
Distance-time graphs show journey information:
- The gradient (slope) represents speed
- A horizontal line indicates the object is stationary
- A straight diagonal line shows constant speed
- A steeper gradient means higher speed
- A curved line indicates changing speed (acceleration or deceleration)
To calculate speed from a distance-time graph, select two points on the line, find the change in distance (vertical axis) and divide by the change in time (horizontal axis).
Speed-time graphs provide different information:
- The gradient represents acceleration
- A horizontal line shows constant speed (zero acceleration)
- A line sloping upward indicates acceleration
- A line sloping downward indicates deceleration
- The area under the graph represents distance travelled
Calculating distance from a speed-time graph requires finding the area under the line. For rectangular sections, multiply speed by time. For triangular sections, use ½ × base × height. Complex graphs may require dividing the area into multiple shapes.
CIE examiners frequently test graph interpretation through multi-part questions worth 5-7 marks, requiring gradient calculations, area determination, and descriptions of motion.
Forces and Newton's laws of motion
Newton's First Law states that 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 car brakes suddenly — their bodies tend to maintain constant velocity due to inertia.
Newton's Second Law provides the fundamental force equation:
Force = mass × acceleration or F = ma
where force is measured in newtons (N), mass in kilograms (kg), and acceleration in m/s².
This equation appears in every CIE IGCSE examination. Common applications include:
- Calculating the force needed to accelerate a car
- Finding the mass of an object given force and acceleration
- Determining acceleration when resultant force and mass are known
For Extended tier, you must understand that the force in F = ma refers specifically to the resultant force — the combined effect of all forces acting on the object.
Newton's Third Law states that when object A exerts a force on object B, object B exerts an equal and opposite force on object A. These forces:
- Are equal in magnitude
- Act in opposite directions
- Act on different objects
- Are the same type of force (both gravitational, both contact forces, etc.)
A common examination scenario involves a book resting on a table. The weight of the book (downward force) and the normal reaction force from the table (upward force) are NOT Newton's third law pairs because they both act on the same object (the book). The actual third law pair involves the book pushing down on the table and the table pushing up on the book.
Weight and mass
Mass measures the quantity of matter in an object, measured in kilograms. Mass remains constant regardless of location.
Weight is the gravitational force acting on an object:
Weight = mass × gravitational field strength or W = mg
On Earth, g = 10 m/s² (or 9.8 m/s² for precise calculations, though CIE typically uses 10 m/s² unless specified).
Weight is measured in newtons and varies with location. An astronaut with mass 80 kg has weight 800 N on Earth but only 133 N on the Moon where g = 1.6 m/s².
Examination questions often require:
- Converting between mass and weight
- Calculating weight on different planets
- Explaining why mass stays constant but weight changes
Friction and air resistance
Friction opposes motion between surfaces in contact. It:
- Acts in the opposite direction to motion
- Converts kinetic energy to thermal energy
- Can be reduced by lubrication or smoother surfaces
- Is greater for rough surfaces and higher normal forces
Air resistance (or drag) opposes motion through air. It:
- Increases with speed
- Increases with cross-sectional area
- Depends on the shape of the object (streamlined shapes reduce drag)
When an object falls, weight (downward) initially exceeds air resistance (upward), producing downward acceleration. As speed increases, air resistance increases until it equals weight. At this point, resultant force becomes zero and the object falls at constant terminal velocity.
CIE questions frequently show velocity-time graphs for falling objects, requiring candidates to identify where acceleration occurs, where terminal velocity is reached, and explain changes in forces throughout the motion.
Momentum and its conservation
For Extended tier, momentum is defined as:
momentum = mass × velocity or p = mv
Momentum is a vector quantity measured in kg m/s.
The principle of conservation of momentum states that in a closed system, the total momentum before a collision equals the total momentum after:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where u represents initial velocities and v represents final velocities.
Examination questions typically involve:
- Two objects colliding and sticking together
- One moving object hitting a stationary object
- Explosions where objects move apart
Velocity direction matters crucially. Assign one direction as positive (typically right or forward) and the opposite direction as negative.
Newton's second law can be expressed in terms of momentum:
Force = rate of change of momentum or F = (mv - mu) / t
This explains why increased collision time reduces force. Car safety features like crumple zones, seat belts and airbags work by increasing collision time, thereby reducing the force experienced by passengers for the same momentum change.
Worked examples
Example 1: Acceleration calculation
A car accelerates from rest to 25 m/s in 8.0 seconds. Calculate the acceleration.
Solution:
Write the equation: a = (v - u) / t
Substitute values: a = (25 - 0) / 8.0
Calculate: a = 3.125 m/s²
Answer: 3.1 m/s² (to 2 significant figures)
Mark scheme: 1 mark for correct equation, 1 mark for correct substitution, 1 mark for answer with unit — total 3 marks
Example 2: Force and motion
A lorry of mass 8000 kg is travelling at 12 m/s. The driver applies the brakes and the lorry stops in 6.0 seconds.
(a) Calculate the deceleration. [3]
(b) Calculate the braking force required. [2]
Solution:
(a) a = (v - u) / t = (0 - 12) / 6.0 = -2.0 m/s²
The deceleration is 2.0 m/s²
(b) F = ma = 8000 × 2.0 = 16 000 N
The braking force is 16 000 N (or 16 kN)
Mark scheme: (a) Correct equation [1], correct substitution [1], answer with unit [1]. (b) Correct use of F = ma [1], correct answer with unit [1]
Example 3: Momentum conservation
A railway truck of mass 5000 kg moving at 4.0 m/s collides with a stationary truck of mass 3000 kg. The trucks couple together. Calculate their combined velocity after collision. [4]
Solution:
Total momentum before = total momentum after
m₁u₁ + m₂u₂ = (m₁ + m₂)v
(5000 × 4.0) + (3000 × 0) = (5000 + 3000)v
20 000 = 8000v
v = 20 000 / 8000 = 2.5 m/s
The combined velocity is 2.5 m/s in the original direction of motion.
Mark scheme: Statement of momentum conservation [1], correct calculation of initial momentum [1], correct equation setup [1], correct final answer with unit [1]
Common mistakes and how to avoid them
Confusing speed and velocity: Speed is scalar (magnitude only), velocity is vector (magnitude and direction). A car travelling around a roundabout at constant speed has changing velocity because direction changes continuously. Always specify direction when discussing velocity.
Incorrect unit conversions: Converting km/h to m/s requires dividing by 3.6, not multiplying by 60. To convert 72 km/h: 72 ÷ 3.6 = 20 m/s. Many candidates multiply by 60 and obtain incorrect answers. Check your answer makes sense — speeds in m/s are typically smaller numbers than speeds in km/h.
Misidentifying Newton's third law pairs: Students often state that weight and normal reaction are third law pairs. They are not — both act on the same object. Third law pairs always act on different objects. For a book on a table, the pairs are: (1) book's weight (Earth pulls book down) and book pulls Earth up; (2) book pushes table down and table pushes book up.
Using mass instead of weight in force calculations: The equation F = ma requires resultant force and mass. Weight is already a force (W = mg), so using F = ma with weight gives incorrect units. When an object falls freely, use a = g = 10 m/s² directly, or calculate weight first then use F = ma where F = W.
Calculating distance-time graph gradient incorrectly: Always use Δdistance / Δtime, taking readings from the graph axes. Many candidates subtract coordinates in reverse order or attempt to use the graph scale divisions without reading actual values. Draw a clear triangle on the graph and label vertical and horizontal measurements.
Forgetting direction in momentum calculations: Momentum is a vector. When objects move in opposite directions, one velocity must be negative. A common error involves treating all velocities as positive, giving incorrect final answers. Establish a positive direction (e.g., right = positive, left = negative) and maintain this throughout the calculation.
Exam technique for Forces and Motion
Command words matter: "Calculate" requires showing equation, substitution and unit (typically 3 marks). "State" needs just the answer (1 mark). "Explain" requires stating what happens and why, using correct physics terminology (2-3 marks). "Describe" needs a detailed account of observations or patterns without necessarily explaining causes.
Show all working for calculations: Even if your final answer is wrong, correct method steps earn partial marks. Write the equation first, substitute values with units on the next line, then calculate. This structure matches CIE mark schemes and maximises credit even for numerical errors.
Graph interpretation questions: When asked to calculate speed from a distance-time graph, show the two coordinates you selected, calculate Δs and Δt separately, then divide. For speed-time graphs, label shapes clearly when finding distance (area under graph) and show calculations for each section separately before adding.
Extended tier candidates: Questions worth 4+ marks typically require application of multiple concepts. A collision problem might need momentum conservation calculation followed by kinetic energy comparison. Read the entire question first to identify all required steps, then work systematically through each part.
Quick revision summary
Speed = distance/time; velocity includes direction. Acceleration = change in velocity/time. Distance-time graph gradient gives speed; speed-time graph gradient gives acceleration and area gives distance. Newton's First Law: objects maintain constant velocity unless acted on by resultant force. F = ma links force, mass and acceleration. Weight = mg where g = 10 m/s² on Earth. Friction and air resistance oppose motion. Terminal velocity occurs when weight equals air resistance. Momentum = mass × velocity; total momentum is conserved in collisions. Always show working in calculations and include units with answers.