Mini Physics
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Speed Acceleration

Calculate average speed over a whole journey and acceleration from a change in speed.

  • SEC G1 Science 2027

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On this page

Effects of Force · about 25–35 min

What you need to understand

Average speed uses the whole journey; acceleration uses the change in speed.

Definitions

speed

distance travelled per unit time

For example: A speed of 5 m/s means 5 metres are travelled each second.
average speed

total distance travelled divided by total time taken

For example: Stops count in the total journey time.
acceleration

change in speed divided by time for the one-direction motion used here

For example: Changing from 2 m/s to 8 m/s in 3 s gives 2 m/s².

Key idea

  1. LookA cyclist speeds up from 2 m/s to 8 m/s in 3 s. Calculate acceleration.
  2. ThinkAverage speed uses the whole journey; acceleration uses the change in speed.
  3. DoIdentify the correct change and units before substituting into the speed or acceleration relationship.

Review the full effects of force topic picture

if you need the visual overview.

Explanation

Speed tells you how much distance is covered per unit time. Average speed = total distance ÷ total time, including any stops within the journey.

Acceleration tells you how quickly speed changes. Find the change in speed first, then divide by the time taken. Its unit is m/s², which is different from the speed unit m/s.

Pause and say it: Average speed uses the whole journey; acceleration uses the change in speed.

Common mistake

Tempting wrong idea: Speed and acceleration both describe how quickly an object is moving.

Why it fails: Speed and acceleration cannot be the same quantity because they answer different questions and have different units.

Use this instead: Speed is distance travelled per unit time. At G1, acceleration is change in speed per unit time; in signed one-dimensional motion, it is change in velocity per unit time.

Practical work

What to show: Identify the correct change and units before substituting into the speed or acceleration relationship.

Before you finish: Do not divide final speed by time when the initial speed is not zero.

Practical link: The topic investigations are taught in

“Distance–time record of a rolling trolley”

(lesson 4) and

“Turning effect and distance from the pivot”

 (lesson 5).

6. Worked Examples

Modelled example 1

Accelerating cyclist

Core

Problem

A cyclist speeds up from 2 m/s to 8 m/s in 3 s. Calculate acceleration.

Study the worked solution

  1. Reason from the evidence

    Method

    Find how much the speed changes before dividing by the time taken.

    Reason

    Average speed uses the whole journey; acceleration uses the change in speed.

    Working

    1. Change in speed = 8 − 2 = 6 m/s.
    2. Acceleration = change in speed ÷ time.
    3. a = 6 ÷ 3 = 2 m/s².

  2. State the conclusion

    Working

    The acceleration is 2 m/s².

Guided practice 2

Calculate two different motion quantities

About 5 min

Problem

A trolley travels 150 m in 30 s. It then changes speed from 3 m/s to 9 m/s in 2 s. Calculate its average speed for the first journey and its acceleration.

Keep the two relationships separate

Hints

Hint 1: first quantity

Average speed uses distance and total time.

Hint 2: second quantity

Find final speed minus initial speed before dividing by time.

View solution step by step

  1. Find average speed

    Method

    Divide the whole distance by the whole stated journey time.

    Reason

    Average speed describes distance covered per unit time.

    Working

    average speed = 150 m ÷ 30 s = 5.0 m/s

  2. Find acceleration

    Method

    Calculate the 6 m/s speed change, then divide by 2 s.

    Reason

    Acceleration measures speed change per unit time.

    Working

    acceleration = (9 − 3) ÷ 2 = 3.0 m/s²

Common misconception 3

Use the change, not only the final speed

Find and correct the mistake

Learner response

A car changes speed from 5 m/s to 11 m/s in 3 s. A learner calculates acceleration as 11 ÷ 3. Spot and correct the error.

Correct the numerator and unit

View solution step by step

  1. Calculate the speed change first

    Method

    Subtract initial speed from final speed.

    Reason

    The starting 5 m/s was already present and is not part of the increase.

    Working

    acceleration = (11 − 5) m/s ÷ 3 s = 2.0 m/s²

Examiner practice 4

A journey with a stop and a speed change

4 marks

Examination question

A cyclist covers 180 m in 30 s and then waits for 15 s. Calculate the average speed for the complete 45 s. The cyclist later changes speed from 4 m/s to 10 m/s in 3 s. Calculate the acceleration. [4 marks]

Show both substitutions and units

View solution step by step

  1. Include the stop in average speed

    2 marks

    Method

    Use 180 m and the complete 45 s.

    Reason

    The waiting time is inside the stated journey.

    Working

    average speed = 180 ÷ 45 = 4.0 m/s

  2. Calculate acceleration

    2 marks

    Method

    Use the 6 m/s change over 3 s.

    Reason

    Acceleration uses change in speed rather than distance.

    Working

    acceleration = (10 − 4) ÷ 3 = 2.0 m/s²

Challenge 5

Choose the quantity from the data

Minimal support

Problem

Object A travels 48 m in 8 s. Object B changes speed from 2 m/s to 14 m/s in 4 s. Calculate the quantity supported by each row and explain why the two answers have different units.

Identify before calculating

Hints

Hint 1: read the columns

Distance and time support speed; two speeds and a time support acceleration.

Hint 2: check the units

One calculation gives metres per second; the other divides that unit by seconds again.

View solution step by step

  1. Calculate each supported quantity

    Method

    Use distance/time for A and change in speed/time for B.

    Reason

    The available evidence determines the relationship.

    Working

    A average speed = 48 ÷ 8 = 6.0 m/s; B acceleration = (14 − 2) ÷ 4 = 3.0 m/s²

Guided practice

Try it with support

A cyclist travels 120 m in 30 s, rests for 10 s, then speeds up from 2 m/s to 8 m/s in 3 s. Find average speed for the stated 40 s and the acceleration.

  1. Include the rest in total time.

  2. Use final speed minus initial speed.

Check the guided answer

Answer: Average speed = 120 ÷ 40 = 3.0 m/s. Acceleration = (8 − 2) ÷ 3 = 2.0 m/s².

Check: Speed and acceleration have different meanings and units.

Practise and continue

Practise this

A trolley covers 200 m in 25 s, then changes speed from 4 m/s to 10 m/s in 2 s. Find its average speed and acceleration.

Need a hint?

  • Write the two relationships before substituting.

Check your answer

Answer: Average speed = 200 ÷ 25 = 8.0 m/s. Acceleration = (10 − 4) ÷ 2 = 3.0 m/s².

Check: Do not divide final speed by time when the initial speed is not zero.

Think like a scientist

What units check distinguishes an acceleration calculation from a speed calculation?

Check the reasoning

Speed has unit m/s. Dividing a change in m/s by seconds gives m/s², the unit of acceleration.

Remember: An answer in m/s cannot be an acceleration.

One-minute check

  1. Hide the page and explain do not mix up speed and acceleration in your own words.

  2. Give a new example that is different from the worked example.

  3. Correct this common mistake: “Speed and acceleration both describe how quickly an object is moving.”

Connect the ideas

Distance–time graphs

Distance–time gradient gives speed; a horizontal section shows rest.

Syllabus and review details

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