Speed, Distance and Time

This lesson covers the speed equation, distance–time graphs and typical speeds, as required by the Edexcel GCSE Combined Science specification (1SC0). Speed is one of the most fundamental ideas in physics and underpins your understanding of motion.

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The Speed Equation

Speed is the distance travelled per unit time. It is a scalar quantity.

$\text{speed} = \frac{\text{distance}}{\text{time}}$speed=timedistance​

$v = \frac{d}{t}$v=td​

where:

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

This can be rearranged:

$d = v \times t$d=v×t

$t = \frac{d}{v}$t=vd​

Exam Tip: Use the formula triangle to rearrange: cover the quantity you want to find. d is on top, v and t are on the bottom. If side by side, multiply; if one is above the other, divide.

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Worked Examples

Example 1: A cyclist travels 600 m in 40 s. What is her speed?

$v = \frac{d}{t} = \frac{600}{40} = 15 \text{ m/s}$v=td​=40600​=15 m/s

Example 2: A car travels at 25 m/s for 120 s. How far does it go?

$d = v \times t = 25 \times 120 = 3000 \text{ m}$d=v×t=25×120=3000 m

Example 3: How long does it take a train at 50 m/s to travel 10 km?

First convert: 10 km = 10 000 m

$t = \frac{d}{v} = \frac{10\,000}{50} = 200 \text{ s}$t=vd​=5010000​=200 s

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Typical Speeds

You should know these approximate values:

Activity / Object	Typical Speed
Walking	1.5 m/s
Running	3 m/s
Cycling	6 m/s
Car in town	13 m/s (≈ 30 mph)
Car on 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 exact typical speeds, but you should be able to recognise reasonable values and spot unreasonable answers. If a question gives a walking speed of 15 m/s, that should ring alarm bells — it is roughly the speed of a sprinter.

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Distance–Time Graphs

A distance–time graph shows how far an object has travelled over time.

Reading the Graph

Feature	What It Tells You
Straight horizontal line	Object is stationary (not moving)
Straight line sloping upward	Object is moving at constant speed
Steeper slope	Faster speed
Curved line (getting steeper)	Object is accelerating
Curved line (getting less steep)	Object is decelerating

Calculating Speed from the Graph

The gradient (slope) of a distance–time graph equals the speed:

$\text{speed} = \text{gradient} = \frac{\Delta d}{\Delta t} = \frac{\text{change in distance}}{\text{change in time}}$speed=gradient=ΔtΔd​=change in timechange in distance​

Worked Example

A distance–time graph shows an object travels from 0 m to 120 m in 30 s in a straight line. What is the speed?

$v = \frac{\Delta d}{\Delta t} = \frac{120 - 0}{30 - 0} = \frac{120}{30} = 4 \text{ m/s}$v=ΔtΔd​=30−0120−0​=30120​=4 m/s

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Average Speed vs Instantaneous Speed

• Average speed is the total distance divided by the total time for a journey.
• Instantaneous speed is the speed at a specific moment.

For a curved distance–time graph, the instantaneous speed at a point equals the gradient of the tangent drawn at that point.

Worked Example

A car travels 100 km at 50 km/h, then 100 km at 100 km/h. What is the average speed?

• Time for first part: t₁ = 100 ÷ 50 = 2 h
• Time for second part: t₂ = 100 ÷ 100 = 1 h
• Total distance = 200 km, Total time = 3 h

$v_{avg} = \frac{200}{3} = 66.7 \text{ km/h}$vavg​=3200​=66.7 km/h

Note: the average speed is not simply (50 + 100) ÷ 2 = 75 km/h. You must use total distance ÷ total time.

Exam Tip: When a distance–time graph is curved, draw a tangent at the point of interest and calculate the gradient of that tangent to find the instantaneous speed.

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Converting Units of Speed

Sometimes you need to convert between m/s and km/h.

m/s → km/h: multiply by 3.6

$v_{km/h} = v_{m/s} \times 3.6$vkm/h​=vm/s​×3.6

km/h → m/s: divide by 3.6

$v_{m/s} = v_{km/h} \div 3.6$vm/s​=vkm/h​÷3.6

Worked Example

Convert 30 m/s to km/h.

$30 \times 3.6 = 108 \text{ km/h}$30×3.6=108 km/h

Convert 90 km/h to m/s.

$90 \div 3.6 = 25 \text{ m/s}$90÷3.6=25 m/s

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Summary

• Speed = distance ÷ time: $v = d / t$v=d/t. Rearrange to find d or t as needed.
• Speed is a scalar; it has no direction.
• Know typical speeds: walking ≈ 1.5 m/s, running ≈ 3 m/s, cycling ≈ 6 m/s, car ≈ 13–30 m/s, sound in air ≈ 330 m/s.
• On a distance–time graph: gradient = speed, horizontal line = stationary, steeper = faster.
• A curved line means changing speed; find instantaneous speed from the gradient of a tangent.
• Average speed = total distance ÷ total time (not the average of two speeds).
• Convert m/s to km/h: multiply by 3.6. Convert km/h to m/s: divide by 3.6.

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Extended Worked Examples with Unit Handling

Example 10: Convert first, then calculate

A commuter cycles 7.2 km in 24 min. Find the average speed in m/s.

• Convert distance: 7.2 km × 10³ = 7200 m.
• Convert time: 24 min × 60 = 1440 s.
• Substitute: $v = d/t = 7200 / 1440 = 5.0$v=d/t=7200/1440=5.0 m/s.

Common-mistake callout: Students often compute 7.2 / 24 = 0.3 and call it "0.3 km/min", which is technically correct but not what the question asks. Always convert to SI base units before dividing.

Example 11: Rearranging to find distance

A runner maintains 4.5 m/s for 12 min. How far do they run?

• Convert time: 12 × 60 = 720 s.
• Rearrange: $d = vt = 4.5 × 720 = 3240$d=vt=4.5×720=3240 m = 3.24 km.

Example 12: Multi-stage journey

A delivery van drives 15 km at 20 m/s, stops for 2 min, then drives 9 km at 15 m/s. Find the average speed for the whole trip.