Speed (AQA GCSE Maths): Revision Notes
Speed
What is speed?
Speed measures how fast something is moving. It tells us the distance covered in a given amount of time. Average speed is the total distance travelled divided by the total time taken.
Speed is a fundamental concept in physics that helps us understand motion. Think of it as the rate at which an object changes its position over time.
The speed formula triangle
The relationship between speed, distance and time can be remembered using a formula triangle.
This triangle shows three key quantities that are interconnected:
- D = Distance
- S = Speed
- T = Time
Mastering this triangle is essential for solving all speed problems!
Using the formula triangle
To find any quantity, cover it up with your finger. The position of the other two quantities gives you the formula:
- Speed = Distance ÷ Time
- Time = Distance ÷ Speed
- Distance = Speed × Time
The basic formula for average speed is:
The beauty of the formula triangle is that it provides a visual way to remember these relationships. Simply cover the quantity you want to find, and the remaining two quantities show you the operation needed.
Units of speed
The most common units for measuring speed are:
- metres per second (m/s)
- kilometres per hour (km/h)
- miles per hour (mph)
The units in your answer will depend on the units you use in the formula. When distance is measured in kilometres and time is measured in hours, speed will be measured in km/h.
Unit Matching is Critical!
Always ensure that your units are consistent throughout your calculation. If speed is given in km/h, your time must be in hours and your distance will be in kilometres.
Converting between minutes and hours
For speed questions, you need to be able to convert between minutes and hours.
Key conversions to remember:
- ½ hour = 30 minutes
- ¾ hour = 45 minutes
- 2¼ hours = 135 minutes
You can also write mixed numbers as decimals. For example, 2¼ hours can be written as '2 hours and 15 minutes' or as minutes total.
Common Conversion Mistake:
Remember that 45 minutes = hour = hour = 0.75 hour
NOT 0.45 hour! This is a frequent error that leads to incorrect answers.
Worked example method
Here's how to solve speed problems step by step:
Worked Example: Finding Distance
A plane travels at a constant speed of 600 km/h for 45 minutes. How far has it travelled?
Step 1: Convert the time to hours 45 minutes = hour = hour
Step 2: Use the formula triangle We want distance, so:
Step 3: Substitute the values
Step 4: State the answer with units The plane has travelled 450 km.
Tips for speed questions
When answering speed questions, follow these essential guidelines:
-
Draw a formula triangle to help you remember the relationships
-
Make sure the units match - convert time to the same units as given in the speed
-
Give units with your answer - don't forget to include the correct units
Unit Consistency Check:
If speed is given in km/h, convert the time into hours by dividing by 60. The units of distance will then be kilometres. This systematic approach prevents unit-related errors.
Remember!
Key Points to Remember:
- Speed = Distance ÷ Time - use the formula triangle to remember this relationship
- Always check your units match before calculating
- Convert time carefully - 45 minutes = ¾ hour, not 0.45 hour
- Include units in your final answer - marks are often lost for missing units
- Show your working clearly - this helps you get method marks even if your final answer is wrong