Introduction to Speed

Hi there! Have you ever wondered why some things seem to zip past you while others move as slowly as a snail? In this chapter, we are going to explore Speed. Speed tells us how fast an object is moving. Whether it's a car racing on a track, a sprinter running a 100-metre dash, or you walking to school, everything that moves has speed!

By the end of these notes, you’ll be a pro at calculating speed and understanding how distance, time, and speed all work together. Don't worry if it seems a bit fast at first—we'll take it one step at a time!

1. Before We Start: Managing Time

To understand speed, we first need to be comfortable with Time. In P6, we often need to switch between hours, minutes, and seconds. Think of it like changing a large dollar bill into smaller coins.

How to Convert Time:

  • Hours to Minutes: Multiply by 60 (because 1 hour = 60 minutes).
  • Minutes to Seconds: Multiply by 60 (because 1 minute = 60 seconds).
  • Minutes to Hours: Divide by 60.

Example: 90 minutes is the same as \( 90 \div 60 = 1.5 \) hours (or \( 1\frac{1}{2} \) hours).

Quick Review Box:

\( 1 \text{ hour} = 60 \text{ minutes} \)
\( 1 \text{ minute} = 60 \text{ seconds} \)
\( 1 \text{ hour} = 3600 \text{ seconds} \)

Key Takeaway: Always check your time units! If a question gives you minutes but asks for speed in "km per hour," you must convert those minutes into hours first.

2. What is Speed?

Speed is the distance moved in a specific amount of time (usually 1 second or 1 hour). If you walk 5 kilometres in 1 hour, your speed is 5 kilometres per hour.

The Magic Speed Triangle

A great way to remember the formulas for Speed, Distance, and Time is to use the DST Triangle. Imagine a triangle with D (Distance) at the top, and S (Speed) and T (Time) at the bottom.

  • To find Distance, look at the bottom: \( \text{Distance} = \text{Speed} \times \text{Time} \)
  • To find Speed, look at D over T: \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)
  • To find Time, look at D over S: \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \)

Memory Trick: Just remember "Don't Stop Talking" (D at the top, S and T at the bottom)!

Did you know?

A Cheetah is the fastest land animal. It can reach a speed of about 30 m/s! That means every single second, it covers 30 metres of ground.

Key Takeaway: Speed is simply Distance divided by Time.

3. Units of Speed: m/s and km/h

In your syllabus, we use two main units to measure how fast things go:

Metres per second (m/s)

This is used for objects moving over shorter distances, like a person running or a ball being thrown. It tells us how many metres an object travels in one second.

Kilometres per hour (km/h)

This is used for faster or long-distance travel, like cars, trains, or airplanes. It tells us how many kilometres an object travels in one hour.

Common Mistake to Avoid: Don't mix your units! If your distance is in kilometres, your time should be in hours. If your distance is in metres, your time should be in seconds. Note: In P6, you are not required to convert between m/s and km/h directly, so focus on getting the units right for each specific problem!

Key Takeaway: Choose m/s for small/short movements and km/h for large/long movements.

4. Solving Speed Problems Step-by-Step

Don't worry if a word problem looks long. Just follow these three simple steps:

  1. Identify: Write down what you know (Distance? Speed? Time?).
  2. Check Units: Make sure the units match (e.g., metres and seconds).
  3. Calculate: Use the Magic Triangle to find the missing piece.

Example Problem: A car travels 150 km in 2 hours. What is its speed?

Step 1: Distance = 150 km, Time = 2 hours.
Step 2: Units are km and hours (they match!).
Step 3: \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)
\( \text{Speed} = 150 \div 2 = 75 \)
Answer: 75 km/h.

Key Takeaway: Always label your final answer with the correct unit (like m/s or km/h) so people know what you are measuring!

5. Reading Travel Graphs

A Travel Graph (or Distance-Time Graph) shows the journey of an object visually. It’s like a "movie" of the trip frozen on paper.

  • The Vertical Axis (Up/Down): Shows the Distance from the starting point.
  • The Horizontal Axis (Left/Right): Shows the Time taken.
  • Steepness (Slope): The steeper the line, the faster the speed.
  • Flat Horizontal Line: This means the distance isn't changing. The object has stopped or is resting.
Analogy:

Think of the graph like a hill. A very steep hill is hard to climb fast—that represents high speed. A flat road is easy to stand still on—that represents being stopped.

Quick Review Box:
Steep Line = Fast
Gentle Line = Slow
Flat Line = Stationary (Stopped)

Key Takeaway: You can tell who is faster just by looking at whose line is steeper!

Summary Checklist

Before you finish your study session, make sure you can:

  • [ ] Convert minutes into hours (by dividing by 60).
  • [ ] Use the DST triangle to find Speed, Distance, or Time.
  • [ ] Identify the difference between m/s and km/h.
  • [ ] Explain what a flat line on a travel graph means.

Great job! Speed can be a tricky topic, but with the DST triangle and careful unit checking, you'll be crossing the finish line in no time!