MotionCambridge IGCSE Physics: Revision notes
Section 1
What is the difference between speed and velocity?
Speed is a scalar quantity that describes how fast an object is travelling, regardless of direction. It is defined as distance travelled per unit time and is calculated using:
v = s/t
where v is speed (m/s), s is distance travelled (m), and t is time taken (s).
Velocity is a vector quantity that describes speed in a given direction. Two objects may have the same speed but different velocities if they are moving in different directions.
For average speed over a complete journey:
average speed = total distance travelled / total time taken
This is useful when an object's speed varies throughout its motion, as it gives an overall picture of the journey.
| Quantity | Type | Definition | Includes Direction? |
|---|---|---|---|
| Speed | Scalar | Distance per unit time | No |
| Velocity | Vector | Speed in a given direction | Yes |
Examiners test whether you understand the difference between scalar and vector. Always state that velocity includes direction whilst speed does not. If a question asks for speed, give a number with units (e.g. 5 m/s); if it asks for velocity, give direction too (e.g. 5 m/s north).
Think of speed as 'how fast' and velocity as 'how fast and which way'. A car doing 60 mph has speed; a car doing 60 mph eastbound has velocity.
Section 2
How do distance–time graphs describe motion?
A distance–time graph plots distance from a starting point against time. The gradient (slope) of the line shows the speed of the object.
Key features:
- A horizontal line (gradient = 0) means the object is at rest (stationary, not moving)
- A straight line with positive gradient means constant speed (the gradient value equals the speed)
- A curved line means the speed is changing (the object is accelerating or decelerating)
- A steeper gradient indicates faster motion
To calculate speed from a distance–time graph:
Choose a straight-line section and use: speed = Δs / Δt (change in distance ÷ change in time)
Measure the vertical change (distance) and horizontal change (time) for a clear section of the line, then divide distance by time.
Note: A straight line that curves upward means acceleration (speed increasing); a curve that flattens means deceleration (speed decreasing).
When reading a distance–time graph, always check if the line is straight or curved. Straight = constant speed (use gradient formula). Curved = changing speed. Never assume direction of change without looking at whether the curve is getting steeper or flatter.
A distance–time graph shows a straight line from (0 s, 0 m) to (5 s, 25 m). Speed = Δs / Δt = (25 − 0) / (5 − 0) = 5 m/s. The object travels at constant speed.
Section 3
What do speed–time graphs show about motion?
A speed–time graph plots velocity (or speed) against time. The gradient shows acceleration, and the area under the line shows distance travelled.
Reading the gradient:
- A horizontal line (gradient = 0) means constant speed (no acceleration)
- An upward sloping line means acceleration (speed increasing)
- A downward sloping line means deceleration (negative acceleration; speed decreasing)
- A steeper gradient indicates faster acceleration
To calculate acceleration from a speed–time graph:
Use: a = Δv / Δt (change in velocity ÷ change in time)
For a straight-line section, measure the vertical change (velocity change) and horizontal change (time), then divide velocity change by time.
Finding distance travelled:
The area under the speed–time curve represents the distance travelled.
- For constant speed (rectangular area): area = speed × time
- For constant acceleration (triangular or trapezoidal area): calculate using geometry
Determining motion type from the graph:
- Horizontal line → constant speed, no acceleration
- Straight diagonal line → constant acceleration
- Curved line → changing acceleration
Examiners often ask you to find distance using the area method. For constant acceleration, the area forms a trapezoid: use area = ½(v₁ + v₂) × t, or split it into a rectangle and triangle. Always show your working.
A speed–time graph shows a straight line from (0 s, 0 m/s) to (4 s, 20 m/s). Acceleration = Δv / Δt = (20 − 0) / (4 − 0) = 5 m/s². Distance = area = ½ × 20 × 4 = 40 m.
Students often confuse gradient direction: on speed–time graphs, an upward slope means acceleration (speed increasing), not deceleration. Downward slope = deceleration (speed decreasing).
Section 4
How do we define and calculate acceleration?
Acceleration is defined as the change in velocity per unit time. It is a vector quantity (has direction) and is calculated using:
a = Δv / Δt
where a is acceleration (m/s²), Δv is change in velocity (m/s), and Δt is change in time (s).
Important points:
- Acceleration can be positive (speed increasing in the direction of motion) or negative (speed decreasing)
- A negative acceleration is called deceleration or retardation
- Constant acceleration occurs when velocity changes at a steady rate (straight line on a speed–time graph)
- Changing acceleration occurs when the rate of velocity change varies (curved line on a speed–time graph)
Free fall acceleration: The acceleration due to gravity near Earth's surface is approximately g = 9.8 m/s² (sometimes rounded to 10 m/s² for calculations). This applies to all objects falling freely in a uniform gravitational field, regardless of mass (ignoring air resistance).
Key distinction:
- Use a = Δv / Δt for any situation
- For free fall: a = g = 9.8 m/s² (downward)
- For motion with constant acceleration: use the gradient of the speed–time graph
When calculating acceleration, always use Δv = v_final − v_initial (final minus initial). If the result is negative, the object is decelerating. State clearly whether acceleration is positive or negative in your answer.
A car slows from 25 m/s to 5 m/s in 4 seconds. Δv = 5 − 25 = −20 m/s, so a = −20 / 4 = −5 m/s². The negative value shows deceleration (the car is slowing down).
Section 5
How does air and liquid resistance affect falling objects?
Falling without resistance: If air resistance is negligible, an object falling freely has constant acceleration equal to g = 9.8 m/s². Velocity increases linearly with time, and the speed–time graph is a straight line.
Falling with air/liquid resistance: When an object falls through air or a liquid, it experiences a resistive force that increases as speed increases (because the object displaces more fluid per unit time). This resistive force opposes motion.
Terminal velocity: Terminal velocity is the maximum speed an object reaches when falling through a fluid (air or liquid). It occurs when:
- The resistive force equals the gravitational force (weight)
- The net force becomes zero
- Acceleration becomes zero (speed no longer increases)
- The object continues at constant velocity
On a speed–time graph:
- Without resistance: straight diagonal line (constant acceleration)
- With resistance: curved line that gradually flattens (acceleration decreases, then becomes zero)
- The curve asymptotically approaches the terminal velocity line
Factors affecting terminal velocity:
- Shape and surface area: larger surface area → higher air resistance → lower terminal velocity
- Density of fluid: denser fluid → higher resistance → lower terminal velocity
- Mass: more massive objects → higher terminal velocity (at same shape and size)
Examples: a feather falls slower than a stone in air (lower terminal velocity); raindrops reach terminal velocity quickly and fall at constant speed; a skydiver reaches terminal velocity before opening a parachute.
Examiners test understanding of why terminal velocity occurs. The key phrase to use is: 'When air resistance equals weight, the net force is zero, so acceleration is zero and the object moves at constant velocity (terminal velocity).'
Think of terminal velocity like a parachutist: initially falling fast and accelerating, but as air resistance builds up, acceleration slows. Eventually, the upward air push equals the downward weight, and the parachutist falls at steady speed (terminal velocity).
Must Know
- Speed = distance ÷ time (v = s/t) and velocity is speed with direction; speed is scalar, velocity is vector
- On distance–time graphs: horizontal line = at rest, straight line = constant speed (gradient = speed), curved line = changing speed
- On speed–time graphs: horizontal line = constant speed, straight line = constant acceleration (gradient = acceleration), area under curve = distance travelled
- Acceleration = change in velocity ÷ time (a = Δv / Δt); negative acceleration is deceleration; constant acceleration gives a straight line on speed–time graph
- Free fall acceleration near Earth ≈ 9.8 m/s² applies to all objects without air resistance
- Terminal velocity occurs when air/liquid resistance equals weight: net force = 0, acceleration = 0, object moves at constant maximum speed; greater surface area or denser fluid → lower terminal velocity
That's the notes covered.
Carry on to the next subtopic.