What you'll learn
Motion forms a foundational topic in CIE IGCSE Physics, examining how objects move and change position over time. This topic appears in both Paper 2 (Core) and Paper 4 (Extended), with questions ranging from graph interpretation to multi-step calculations using equations of motion. Mastering motion concepts is essential for understanding forces, energy and momentum in later topics.
Key terms and definitions
Distance — the total length of the path travelled by an object, measured in metres (m). Distance is a scalar quantity with magnitude only.
Displacement — the straight-line distance from the starting point to the finishing point in a specific direction, measured in metres (m). Displacement is a vector quantity with both magnitude and direction.
Speed — the distance travelled per unit time, calculated as distance ÷ time, measured in metres per second (m/s) or kilometres per hour (km/h). Speed is a scalar quantity.
Velocity — the rate of change of displacement, or speed in a specified direction, measured in m/s. Velocity is a vector quantity.
Acceleration — the rate of change of velocity, measured in metres per second squared (m/s²). Acceleration can be positive (speeding up) or negative, also called deceleration or retardation (slowing down).
Uniform acceleration — constant acceleration where the velocity increases by equal amounts in equal time intervals.
Average speed — the total distance travelled divided by the total time taken for a complete journey.
Core concepts
Calculating speed, distance and time
The fundamental relationship for motion is:
speed = distance ÷ time or v = s ÷ t
This can be rearranged using the triangle method:
- distance = speed × time (s = v × t)
- time = distance ÷ speed (t = s ÷ v)
When calculating average speed for journeys with multiple stages:
average speed = total distance ÷ total time
A common error is to average the speeds from different stages rather than using total values. For example, if a car travels 100 km at 50 km/h then 100 km at 100 km/h, the average speed is NOT 75 km/h. The first stage takes 2 hours, the second takes 1 hour, so average speed = 200 km ÷ 3 hours = 66.7 km/h.
Understanding acceleration
Acceleration measures how quickly velocity changes:
acceleration = change in velocity ÷ time taken
or a = (v - u) ÷ t
where:
- a = acceleration (m/s²)
- v = final velocity (m/s)
- u = initial velocity (m/s)
- t = time (s)
This rearranges to: v = u + at
Key points about acceleration:
- An object moving at constant speed in a circle is accelerating because its direction (and therefore velocity) is changing
- Deceleration is negative acceleration
- Free fall acceleration due to gravity is approximately 10 m/s² (or 9.8 m/s² for more precise calculations)
Distance-time graphs
Distance-time graphs show how distance from a starting point changes over time. The gradient (slope) of the line represents speed.
Interpreting distance-time graphs:
- Horizontal line → stationary (zero speed)
- Straight diagonal line → constant speed (uniform motion)
- Steep gradient → high speed
- Shallow gradient → low speed
- Curved line → changing speed (acceleration or deceleration)
To calculate speed from a distance-time graph:
speed = gradient = rise ÷ run = change in distance ÷ change in time
For curved sections, draw a tangent to the curve at the required point and calculate the gradient of that tangent to find instantaneous speed.
Velocity-time graphs
Velocity-time graphs are more powerful analytical tools that show how velocity changes with time. Several key features can be extracted:
The gradient represents acceleration:
- acceleration = change in velocity ÷ change in time
- Steep gradient → large acceleration
- Horizontal line → constant velocity (zero acceleration)
- Negative gradient → deceleration
The area under the graph represents displacement:
- For rectangular sections: area = length × width = velocity × time
- For triangular sections: area = ½ × base × height
- For complex shapes, divide into rectangles and triangles
Common velocity-time graph patterns:
- Horizontal line → constant velocity (uniform motion)
- Positive slope → acceleration
- Negative slope → deceleration
- Curved line → non-uniform acceleration
When calculating total displacement from a velocity-time graph with sections above and below the time axis, areas below the axis represent motion in the opposite direction and should be subtracted.
Equations of motion (Extended tier only)
Four equations connect displacement, initial velocity, final velocity, acceleration and time for objects moving with uniform acceleration:
- v = u + at
- s = ½(u + v)t
- s = ut + ½at²
- v² = u² + 2as
where:
- s = displacement (m)
- u = initial velocity (m/s)
- v = final velocity (m/s)
- a = acceleration (m/s²)
- t = time (s)
Choosing the correct equation:
Each equation omits one variable. Select the equation that:
- Contains the three quantities you know
- Contains the one quantity you need to find
- Does NOT contain the quantity you neither know nor need
For example, if you know u, a and s, and need to find v, use v² = u² + 2as (which omits t).
Sign conventions:
Choose a positive direction (usually the direction of initial motion). Quantities in that direction are positive; quantities in the opposite direction are negative. Deceleration is represented as negative acceleration.
Analysing real-world motion
Free fall motion:
Objects falling under gravity (ignoring air resistance) have:
- Initial velocity u = 0 (if dropped from rest)
- Acceleration a = 10 m/s² (or g = 9.8 m/s²) downward
- The equations of motion apply directly
Projectile motion:
Horizontal and vertical components of motion are independent:
- Horizontal velocity remains constant (no horizontal acceleration)
- Vertical motion experiences acceleration due to gravity
- At maximum height, vertical velocity = 0
Vehicle stopping distances:
Total stopping distance = thinking distance + braking distance
- Thinking distance = distance travelled during reaction time (typically 0.2-0.7 seconds) = speed × reaction time
- Braking distance = distance travelled while braking to rest, depends on speed² and deceleration
Factors increasing stopping distance:
- Greater initial speed (braking distance increases with speed²)
- Longer reaction time (tiredness, alcohol, distractions)
- Poor road conditions (rain, ice reduce friction)
- Poor vehicle condition (worn brakes or tyres)
Worked examples
Example 1: Average speed calculation
Question: A cyclist travels 15 km in 30 minutes, stops for 15 minutes, then travels a further 10 km in 20 minutes. Calculate the average speed for the whole journey in m/s. [3 marks]
Solution:
Total distance = 15 km + 10 km = 25 km = 25,000 m [1]
Total time = 30 min + 15 min + 20 min = 65 min = 65 × 60 = 3,900 s [1]
Average speed = 25,000 ÷ 3,900 = 6.4 m/s [1]
Note: The stop time must be included in total time.
Example 2: Velocity-time graph interpretation
Question: The velocity-time graph shows the motion of a train between two stations.
[Graph shows: 0-20s acceleration from 0 to 30 m/s; 20-80s constant at 30 m/s; 80-100s deceleration to 0 m/s]
(a) Calculate the acceleration during the first 20 seconds. [2 marks]
(b) Calculate the total distance travelled. [3 marks]
Solution:
(a) acceleration = change in velocity ÷ time [1] = (30 - 0) ÷ 20 = 1.5 m/s² [1]
(b) Split into three sections:
Section 1 (triangle): area = ½ × 20 × 30 = 300 m [1]
Section 2 (rectangle): area = 60 × 30 = 1,800 m [1]
Section 3 (triangle): area = ½ × 20 × 30 = 300 m
Total distance = 300 + 1,800 + 300 = 2,400 m or 2.4 km [1]
Example 3: Equations of motion (Extended)
Question: A car travelling at 25 m/s brakes with uniform deceleration and comes to rest after travelling 80 m. Calculate:
(a) the deceleration [3 marks]
(b) the time taken to stop [2 marks]
Solution:
(a) Known: u = 25 m/s, v = 0 m/s, s = 80 m; Find: a
Use v² = u² + 2as [1]
0² = 25² + 2 × a × 80
0 = 625 + 160a
a = -625 ÷ 160 = -3.9 m/s² [1]
Deceleration = 3.9 m/s² [1]
(b) Use v = u + at [1]
0 = 25 + (-3.9) × t
t = 25 ÷ 3.9 = 6.4 s [1]
Common mistakes and how to avoid them
Confusing distance with displacement — Distance is the total path length (always positive); displacement is the straight-line distance with direction (can be zero even after a long journey if you return to the start). Read questions carefully to identify which is required.
Averaging speeds incorrectly — Never average two different speeds to find average speed. Always use average speed = total distance ÷ total time. Calculate the time for each stage separately, then use totals.
Wrong units — Speed questions often give distance in kilometres and require answers in m/s, or vice versa. Convert systematically: 1 km = 1,000 m; 1 hour = 3,600 s; to convert km/h to m/s, divide by 3.6.
Misreading graph axes — Always check what each axis represents. Distance-time and displacement-time graphs look similar but gradient meanings differ. Check scales carefully; axes may not start at zero.
Forgetting that area under velocity-time graph is displacement, not distance — If velocity becomes negative (motion reverses direction), the area below the time axis should be subtracted when finding total displacement but added when finding total distance travelled.
Using wrong equation of motion — List what you know and what you need to find before selecting an equation. Check your chosen equation contains exactly those four variables and omits the fifth. Ensure signs are correct: choose a positive direction and stick to it.
Exam technique for Motion
Graph drawing and interpretation questions — When asked to sketch graphs, use a ruler for straight sections and ensure curves are smooth. Label axes with quantities and units. When calculating gradients, show the triangle on the graph, mark coordinates clearly, and write gradient = rise ÷ run with values substituted.
Multi-step calculations — Extended tier questions often require using one equation to find an intermediate value, then using that result in another equation. Write down what you know after each step. Show all working clearly so method marks are awarded even if the final answer is wrong.
Command word awareness — "Calculate" requires a numerical answer with working and units. "State" needs a short answer without explanation. "Explain" requires reasoning, often linking cause and effect. "Sketch" means draw approximate shape showing key features; precision is not required.
Unit conversion and significant figures — CIE mark schemes typically accept answers to 2 or 3 significant figures. Show unit conversions as separate steps. Include units with all final answers; this is often a mark on its own.
Quick revision summary
Motion describes how objects change position over time. Speed = distance ÷ time (scalar); velocity = displacement ÷ time (vector). Acceleration = change in velocity ÷ time. Distance-time graph gradients give speed; velocity-time graph gradients give acceleration and areas give displacement. Extended tier students must know four equations of motion for uniform acceleration: v = u + at; s = ½(u + v)t; s = ut + ½at²; v² = u² + 2as. Average speed uses total distance and total time. Always check units and show full working for method marks.