Speed and Velocity

This lesson covers speed, velocity, and distance-time graphs — as required by the Edexcel GCSE Physics specification (1PH0), Topic 1: Key Concepts of Physics. You need to be able to calculate speed and velocity, recall typical speeds, and interpret distance-time graphs.

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Speed

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

speed = distance ÷ time

$s = \frac{d}{t}$s=td​

Where:

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

This can be rearranged:

• d = s × t (distance = speed × time)
• t = d ÷ s (time = distance ÷ speed)

Exam Tip: Remember the formula triangle — put d on top, s and t on the bottom. Cover the quantity you want to find: d = s × t, s = d/t, t = d/s.

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Velocity

Velocity is a vector quantity — it is the speed in a given direction, or more precisely, the rate of change of displacement.

velocity = displacement ÷ time

$v = \frac{x}{t}$v=tx​

Where:

• v = velocity (m/s)
• x = displacement (m)
• t = time (s)

Important Difference

• A car driving around a circular track at 20 m/s has a constant speed of 20 m/s, but its velocity is constantly changing because its direction is constantly changing.
• An object that returns to its starting point has an average velocity of zero (displacement = 0), even though its average speed was not zero.

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Typical Speeds

You need to know typical values of speed for the following. These are approximate values — you will not be penalised for slight variations.

Activity/Object	Typical Speed
Walking	~1.5 m/s
Running	~3 m/s
Cycling	~6 m/s
Car (town driving)	~13 m/s (~30 mph)
Car (motorway)	~30 m/s (~70 mph)
Train	~50 m/s
Aeroplane	~250 m/s
Speed of sound in air	~330 m/s

Exam Tip: You do not need to memorise these to the nearest decimal place. Approximate values are acceptable. However, know them well enough to recognise unreasonable answers — for example, a person cannot run at 30 m/s, and a car cannot travel at 330 m/s.

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Calculating Average Speed

Average speed is calculated over an entire journey:

average speed = total distance ÷ total time

Worked Example 1

A cyclist rides 12 km in 40 minutes. Calculate her average speed in m/s.

Step 1: Convert to SI units.

• Distance = 12 km = 12 000 m
• Time = 40 min = 40 × 60 = 2400 s

Step 2: Apply the formula.

• Average speed = 12 000 ÷ 2400 = 5.0 m/s

Worked Example 2

A car travels 80 km at 40 km/h and then 80 km at 80 km/h. What is the average speed for the whole journey?

Step 1: Find the time for each part.

• Time 1 = 80 ÷ 40 = 2 hours
• Time 2 = 80 ÷ 80 = 1 hour

Step 2: Find total distance and total time.

• Total distance = 80 + 80 = 160 km
• Total time = 2 + 1 = 3 hours

Step 3: Calculate average speed.

• Average speed = 160 ÷ 3 = 53.3 km/h

Note: The average speed is not simply (40 + 80) ÷ 2 = 60 km/h. This is a common mistake.

Exam Tip: Never just average the two speeds. Always calculate total distance ÷ total time. This is a very common exam error.

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Distance-Time Graphs

A distance-time graph shows how the distance travelled by an object changes with time. These graphs are essential for interpreting motion.

How to Read a Distance-Time Graph

Feature of the Graph	What It Means
Horizontal line	Object is stationary (not moving)
Straight diagonal line (upward slope)	Object is moving at constant speed
Steeper gradient	Higher speed
Curved line (curving upward)	Object is accelerating (speed increasing)
Curved line (levelling off)	Object is decelerating (speed decreasing)

The Gradient = Speed

The gradient (slope) of a distance-time graph gives the speed:

speed = gradient = change in distance ÷ change in time

$\text{speed} = \frac{\Delta d}{\Delta t}$speed=ΔtΔd​

Interpreting a Journey

graph LR
    A["A: Stationary<br/>(horizontal line)"] --> B["B: Constant speed<br/>(straight diagonal)"]
    B --> C["C: Stationary again<br/>(horizontal line)"]
    C --> D["D: Faster constant speed<br/>(steeper diagonal)"]

    style A fill:#2c3e50,color:#fff
    style B fill:#2980b9,color:#fff
    style C fill:#e67e22,color:#fff
    style D fill:#27ae60,color:#fff

In a typical exam journey graph:

• Section A: Object is stationary — distance is not changing.
• Section B: Object moves at constant speed — gradient is constant.
• Section C: Object stops again — another horizontal section.
• Section D: Object moves at a higher speed — steeper gradient.

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Calculating Speed from a Distance-Time Graph

Worked Example

From a distance-time graph, the object travels from 0 m to 120 m in 30 seconds (a straight line). What is its speed?

Speed = gradient = (120 − 0) ÷ (30 − 0) = 120 ÷ 30 = 4.0 m/s

Finding Speed on a Curved Section

If the line is curved, the speed is changing. To find the speed at a particular instant, draw a tangent to the curve at that point and calculate the gradient of the tangent.

1. Place a ruler so it just touches the curve at the point of interest.
2. Draw a straight line along the ruler.
3. Choose two points on the tangent line that are far apart.
4. Calculate: gradient = rise ÷ run = Δd ÷ Δt.