Speed, Distance and Time

This lesson covers the relationship between speed, distance and time as required by AQA GCSE Combined Science Trilogy (8464), section 6.5.2. You will learn the key equation, how to rearrange it, typical speeds for everyday situations, and how to interpret distance-time graphs.

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The Speed Equation

The equation linking speed, distance and time is:

$s = \frac{d}{t}$s=td​

Where:

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

This equation is on the AQA equation sheet, but you should know it from memory.

Rearranging the Equation

To find	Rearranged equation
Speed	$s = d / t$s=d/t
Distance	$d = s \times t$d=s×t
Time	$t = d / s$t=d/s

Exam Tip: Use the formula triangle to help rearrange. Place d on top, and s and t on the bottom. Cover the quantity you want to find — the remaining two tell you what to do.

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Typical Speeds

AQA expects you to know typical values for everyday speeds.

Activity / Object	Typical Speed
Walking	1.5 m/s
Running	3 m/s
Cycling	6 m/s
Car in a town	13 m/s (≈ 30 mph)
Car on a motorway	30 m/s (≈ 70 mph)
Train	50 m/s
Sound in air	340 m/s
Wind speed	5–20 m/s

Exam Tip (AQA 8464): You do not need to memorise these values to the nearest decimal place, but you should know the approximate order of magnitude. A question might ask you to judge whether a calculated speed is "reasonable."

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Worked Examples

Example 1 — Calculating Speed

A cyclist travels 240 m in 40 s. Calculate the speed.

Solution:

$s = \frac{d}{t} = \frac{240}{40} = 6$s=td​=40240​=6 m/s

Example 2 — Calculating Distance

A car travels at 25 m/s for 2 minutes. Calculate the distance.

Solution:

First convert time: 2 minutes = 120 s

$d = s \times t = 25 \times 120 = 3000$d=s×t=25×120=3000 m (or 3 km)

Example 3 — Calculating Time

A jogger runs at 3 m/s and covers 900 m. How long does the journey take?

Solution:

$t = \frac{d}{s} = \frac{900}{3} = 300$t=sd​=3900​=300 s (or 5 minutes)

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Distance-Time Graphs

A distance-time graph plots distance (y-axis) against time (x-axis). The key rules for reading these graphs are:

Feature of the graph	What it means
Horizontal line	Object is stationary (not moving)
Straight line with positive gradient	Constant speed
Steeper straight line	Faster constant speed
Curve getting steeper	Accelerating (speeding up)
Curve getting shallower	Decelerating (slowing down)

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

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

graph LR
    subgraph "Distance-Time Graph Interpretation"
        A["Flat line → Stationary"]
        B["Straight slope → Constant speed"]
        C["Steeper slope → Faster speed"]
        D["Curve steepening → Accelerating"]
    end

    style A fill:#e74c3c,color:#fff
    style B fill:#2980b9,color:#fff
    style C fill:#8e44ad,color:#fff
    style D fill:#27ae60,color:#fff

Worked Example — Reading a Distance-Time Graph

A graph shows an object that travels 200 m in the first 20 s, then remains stationary for 10 s.

(a) What is the speed during the first 20 s?

$s = \frac{200}{20} = 10$s=20200​=10 m/s

(b) What is the speed during the stationary period?

$s = 0$s=0 m/s (the line is horizontal, so the gradient is zero)

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Average Speed vs Instantaneous Speed

• Average speed = total distance ÷ total time. It gives the overall speed for an entire journey.
• Instantaneous speed = speed at a specific moment in time. On a distance-time graph, it is the gradient of the tangent to the curve at that point.

For straight-line sections, average speed and instantaneous speed are the same. For curved sections, you must draw a tangent.

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Unit Conversions

Conversion	Method
km to m	Multiply by 1000
m to km	Divide by 1000
hours to seconds	Multiply by 3600
minutes to seconds	Multiply by 60
km/h to m/s	Divide by 3.6
m/s to km/h	Multiply by 3.6

Worked Example

Convert 72 km/h to m/s.

$72 \div 3.6 = 20$72÷3.6=20 m/s

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Common Mistakes

• Forgetting to convert units (e.g. minutes to seconds or km to m) before substituting into the equation.
• Confusing the gradient of a distance-time graph (speed) with the gradient of a velocity-time graph (acceleration).
• Writing speed with a direction — speed is scalar and has no direction.
• Reading graph axes incorrectly — always check the scale carefully.

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Summary

• The speed equation is $s = d / t$s=d/t.
• Know typical speeds: walking ~1.5 m/s, running ~3 m/s, cycling ~6 m/s, car ~13–30 m/s.
• On a distance-time graph, the gradient = speed. A horizontal line = stationary. A straight line = constant speed. A curve = changing speed.
• Average speed = total distance ÷ total time.
• Always convert units before calculating.

Exam Tip (AQA 8464): Many AQA questions give times in minutes or distances in km. If the answer requires m/s, you MUST convert before calculating. Forgetting unit conversion is the single most common error in speed calculations.

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Extended Worked Examples

Worked Example 1: Multi-Stage Journey

A runner completes a race in three stages.

• Stage 1: 400 m in 80 s
• Stage 2: 300 m in 75 s
• Stage 3: 100 m in 20 s

Calculate (a) the speed during each stage, and (b) the average speed for the whole race.

Solution: