Speed and Velocity

This lesson covers speed, velocity, and the equations of motion as required by the AQA GCSE Physics specification (4.5.6). Speed tells us how fast an object is moving, while velocity tells us both how fast and in which direction. These concepts are fundamental to understanding all aspects of motion and forces.

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Speed

Speed is a scalar quantity that tells you how fast an object is moving. It is defined as the distance travelled per unit time.

The equation for speed is:

s = d / t

Where:

• s = speed (m/s)
• d = distance (m)
• t = time (s)

This equation can be rearranged:

• To find distance: d = s x t
• To find time: t = d / s

Exam Tip: The speed equation s = d / t is NOT on the AQA equation sheet — you must memorise it. Use the formula triangle: put d on top, and s and t on the bottom. Cover the quantity you want to find.

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Typical Speeds

You must know typical speeds for different objects and situations. These are approximate values.

Object/Situation	Typical Speed (m/s)	Typical Speed (km/h)
Walking	1.5	5.4
Running	3	10.8
Cycling	6	21.6
Car in town	13	48
Car on motorway	31	112
Train	55	200
Aeroplane	250	900
Speed of sound in air	330	1190

Factors Affecting Speed

The speed at which a person can walk, run, or cycle depends on:

• Age — younger adults tend to be faster than the very young or elderly.
• Fitness — fitter people can sustain higher speeds.
• Terrain — uphill is slower than flat; rough ground is slower than smooth.
• Distance — speed typically decreases over longer distances (fatigue).
• Weather — headwinds slow you down; tailwinds speed you up.

Exam Tip: You do not need to memorise exact typical speeds, but you should know the approximate order of magnitude. A person walks at about 1.5 m/s, runs at about 3 m/s, and cycles at about 6 m/s. Cars travel at about 13 m/s in town and 31 m/s on the motorway. The speed of sound in air is about 330 m/s.

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Velocity

Velocity is a vector quantity that tells you the speed of an object in a given direction.

velocity = displacement / time

The key difference between speed and velocity:

Feature	Speed	Velocity
Type	Scalar	Vector
Has direction?	No	Yes
Measures	Distance / time	Displacement / time
Can be negative?	No	Yes (opposite direction)
Units	m/s	m/s

An object can have a constant speed but a changing velocity — this happens when the object changes direction. For example, a car going around a roundabout at a constant speed has a constantly changing velocity because its direction is constantly changing.

Exam Tip: If an object is moving in a circle at constant speed, it is accelerating because its velocity (direction) is changing. This is a common exam question — do not confuse constant speed with constant velocity.

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Calculating Speed and Velocity

Example 1: Average Speed

A cyclist travels 240 m in 40 s. What is the cyclist's average speed?

s = d / t s = 240 / 40 s = 6 m/s

Example 2: Finding Distance

A car travels at a speed of 20 m/s for 30 seconds. How far does it travel?

d = s x t d = 20 x 30 d = 600 m

Example 3: Finding Time

A runner covers 1500 m at an average speed of 5 m/s. How long does the run take?

t = d / s t = 1500 / 5 t = 300 s (5 minutes)

Example 4: Converting Units

To convert km/h to m/s: divide by 3.6

A car travels at 72 km/h. What is this in m/s?

72 / 3.6 = 20 m/s

To convert m/s to km/h: multiply by 3.6

A train travels at 50 m/s. What is this in km/h?

50 x 3.6 = 180 km/h

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The Speed Equation Triangle

The formula triangle helps you rearrange the equation quickly:

graph TD
    D["d (distance)"] --> ST["s x t"]
    ST --> S["s = d / t"]
    ST --> T["t = d / s"]

    style D fill:#2c3e50,color:#fff
    style ST fill:#2980b9,color:#fff

• Cover d to get s x t (distance = speed x time).
• Cover s to get d / t (speed = distance / time).
• Cover t to get d / s (time = distance / speed).

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Relative Motion

When two objects are moving, their relative speed depends on whether they are moving in the same direction or opposite directions.

Situation	Relative Speed
Two objects moving in the same direction	Subtract the speeds
Two objects moving in opposite directions	Add the speeds

Example: Relative Motion

Car A travels at 30 m/s northbound. Car B travels at 25 m/s northbound (same direction).

Relative speed of car A with respect to car B = 30 - 25 = 5 m/s

Car A travels at 30 m/s northbound. Car C travels at 25 m/s southbound (opposite direction).

Relative speed of car A with respect to car C = 30 + 25 = 55 m/s

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Circular Motion and Changing Velocity

An object moving in a circle at constant speed has a constantly changing velocity because its direction is continuously changing. Since velocity is a vector, any change in direction means a change in velocity, which means the object is accelerating — even though its speed remains the same.

This acceleration towards the centre of the circle requires a resultant force directed towards the centre. This force is called the centripetal force.

graph TD
    subgraph "Circular Motion"
        C["Centre"] -->|"Centripetal force"| O["Object on circular path"]
        O -->|"Velocity (tangent)"| T["Direction of motion"]
    end

    style C fill:#e74c3c,color:#fff
    style O fill:#2980b9,color:#fff
    style T fill:#27ae60,color:#fff