Let's Learn About Speed!

Hello, Maths Explorers! Have you ever wondered how fast a car is going, or who is the quickest runner in your class? That's all about speed! In these notes, we'll go on an exciting journey to understand what speed is, how we can measure it, and how it helps us in our everyday lives. It's a super useful part of Maths that you see everywhere. Don't worry if it sounds tricky, we'll learn it all one step at a time!

The Building Blocks: Distance and Time

Before we can talk about speed, we need to be experts on its two best friends: Distance and Time.

What is Distance?

Distance is simply how far something has travelled. It's the length between two points.

For example, the distance from your home to school might be 2 kilometres. The length of a swimming pool might be 50 metres.

We often measure distance in:
• Metres (m) for shorter distances.
• Kilometres (km) for longer distances.

What is Time?

Time is how long it takes for something to happen.

We measure time in:
• Seconds (s) for very short periods.
• Minutes (min)
• Hours (h) for longer periods.

Super Skill: Converting Time!

Sometimes, we need to change time from one unit to another. It's like swapping one type of coin for another! Here's the secret code:

To change from a BIGGER unit to a SMALLER unit, we MULTIPLY.
• Hours to Minutes: Multiply by 60 (because there are 60 minutes in 1 hour).
Example: 2 hours = 2 × 60 = 120 minutes.
• Minutes to Seconds: Multiply by 60 (because there are 60 seconds in 1 minute).
Example: 3 minutes = 3 × 60 = 180 seconds.

To change from a SMALLER unit to a BIGGER unit, we DIVIDE.
• Seconds to Minutes: Divide by 60.
Example: 180 seconds = 180 ÷ 60 = 3 minutes.
• Minutes to Hours: Divide by 60.
Example: 90 minutes = 90 ÷ 60 = 1.5 hours. That's one and a half hours!

Key Takeaway: Understanding distance and time is the first step to becoming a speed master. Remember the magic number 60 for converting time!

Understanding Speed

What is Speed?

Speed is a measure of how quickly something is moving. It tells us the distance something travels in a certain amount of time.

Think about two runners in a race.
• If they both run for 10 seconds, the runner who covers more distance is going faster.
• If they both run 100 metres, the runner who takes less time is going faster.

So, speed connects distance and time together!

Speed's Special Units

We use special units to describe speed. You've probably heard them before!

1. Kilometres per hour (km/h)
This tells you how many kilometres are travelled in one hour. It's often used for cars, buses, and trains.
Example: A car travelling at 50 km/h will cover a distance of 50 km if it drives for a full hour.

2. Metres per second (m/s)
This tells you how many metres are travelled in one second. It's great for things that move quickly over short distances, like a sprinter or a thrown ball.
Example: A world-class sprinter can run at about 10 m/s. That's 10 metres every single second!

Important Note: For your problems, you will either work with km/h or m/s. You will not need to convert between them, so no need to worry about that!

Did you know? The fastest land animal is the cheetah, which can reach speeds of over 100 km/h! That's faster than cars are allowed to go on many city roads!

The Magic Speed Triangle!

This is the best trick for solving speed problems! Imagine a triangle split into three parts. Distance (D) is at the top. Speed (S) and Time (T) are at the bottom.

To find the formula for what you need, just cover it up with your finger!
• Want to find Speed? Cover 'S'. You see 'D' over 'T'. So, Speed = Distance ÷ Time.
• Want to find Distance? Cover 'D'. You see 'S' next to 'T'. So, Distance = Speed × Time.
• Want to find Time? Cover 'T'. You see 'D' over 'S'. So, Time = Distance ÷ Speed.

How to Find Speed

Formula: $$Speed = {Distance \over Time}$$
Problem: A family drives 200 km to the beach. The journey takes 4 hours. What was their average speed?
Step 1: Write down what you know. Distance = 200 km. Time = 4 hours.
Step 2: Use the formula. Speed = 200 km ÷ 4 h.
Step 3: Calculate the answer. 200 ÷ 4 = 50.
Answer: The family's average speed was 50 km/h.

How to Find Distance

Formula: $$Distance = Speed \times Time$$
Problem: A girl cycles at a steady speed of 12 km/h. How far can she cycle in 3 hours?
Step 1: Write down what you know. Speed = 12 km/h. Time = 3 hours.
Step 2: Use the formula. Distance = 12 km/h × 3 h.
Step 3: Calculate the answer. 12 × 3 = 36.
Answer: She can cycle 36 km.

How to Find Time

Formula: $$Time = {Distance \over Speed}$$
Problem: A tortoise is crawling to a yummy lettuce leaf that is 10 metres away. If the tortoise crawls at a speed of 2 metres per minute, how long will it take him?
Step 1: Write down what you know. Distance = 10 m. Speed = 2 m/min.
Step 2: Use the formula. Time = 10 m ÷ 2 m/min.
Step 3: Calculate the answer. 10 ÷ 2 = 5.
Answer: It will take the tortoise 5 minutes.

Watch Out! Common Mistakes: Always check your units! If speed is in km/h, your distance must be in km and your time must be in hours. If you are given time in minutes, you must convert it to hours first by dividing by 60!

Travel Graphs - A Story of a Journey

What is a Travel Graph?

A travel graph (or distance-time graph) is a picture that tells the story of a journey. It shows how far someone has travelled at different points in time.

• The line going along the bottom (horizontal axis) shows Time.
• The line going up the side (vertical axis) shows Distance from the start.

How to Read a Travel Graph

The shape of the line tells you what's happening!
• A line sloping upwards means the person is moving away from the start.
• A steeper line means they are moving faster!
• A flat, horizontal line means the person has stopped for a rest. Time is passing, but their distance isn't changing.

Let's imagine a graph... A line starts at zero, goes up to '30 km' in '2 hours'. Then, the line becomes flat for '1 hour'. Finally, it goes up again to '50 km' in the next hour (at the '4 hour' mark).

Questions about this journey:
1. How far did the person travel in the first 2 hours?
Answer: Look at the 2-hour mark on the bottom and see where the line is. It's at 30 km.

2. How long did the person rest for?
Answer: The line is flat between 2 hours and 3 hours. So, they rested for 1 hour.

3. What was the total distance of the journey?
Answer: Look at where the line ends. It ends at 50 km.

Key Takeaway: A travel graph tells a story. Up means moving, flat means resting, and steep means fast!

You're a Speed Master!

Great job! You've learned all the key ideas about Speed, Distance, and Time.

Quick Review:
• Speed is how fast you travel (Distance ÷ Time).
• The magic Speed Triangle helps you find the formulas for Speed, Distance, and Time.
• The main units are km/h and m/s.
• A travel graph shows a journey's story with lines.

Keep practising, and soon you'll be solving speed problems faster than a cheetah! Well, maybe not that fast. Keep up the amazing work!