Welcome to P4.2: How can we describe motion?

In this chapter, we are going to learn how to put numbers and names to things that move. Whether it’s a snail crawling across a leaf or a rocket zooming into space, Physics uses the same set of rules to describe them! By the end of these notes, you’ll be able to calculate how fast things go, how quickly they speed up, and how to read "motion stories" told through graphs.

Don't worry if this seems tricky at first! We’ll take it one step at a time, and once you see the patterns, it becomes much easier.


1. Distance vs. Displacement: Where are you exactly?

To describe motion, we first need to know how far something has moved. In Physics, we have two ways of saying this:

  • Distance: This is just "how much ground you covered." It doesn't matter what direction you went. If you walk 10m forward and 10m back, your distance is 20m.
  • Displacement: This is "how far out of place you are." It is the straight-line distance from where you started to where you ended, including the direction. If you walk 10m forward and 10m back, your displacement is 0m because you’re back where you started!
Scalars and Vectors

This brings us to a very important distinction in Physics:

  • Scalar quantities: These only have a magnitude (size). Examples: Distance, speed, mass, and time.
  • Vector quantities: These have both magnitude (size) AND direction. Examples: Displacement, velocity, and acceleration.

Memory Tip: Vector starts with V for Very important direction!

Key Takeaway: Use distance and speed for simple totals, but use displacement and velocity when you need to know exactly where something is going.


2. Speed: How fast are you going?

Speed is a scalar quantity. It tells us how much distance is covered in a certain amount of time. To find the average speed, we use this formula:

\( \text{average speed (m/s)} = \frac{\text{distance (m)}}{\text{time (s)}} \)

Typical Speeds You Should Know

In your exam, you might be asked to estimate a speed. Here are the typical values for everyday life:

  • Walking: \( \approx 1.5 \, m/s \)
  • Running: \( \approx 3.0 \, m/s \)
  • Cycling: \( \approx 6.0 \, m/s \)
  • Speed of Sound in air: \( \approx 330 \, m/s \)
  • Wind: \( \approx 5-20 \, m/s \)
Converting Units

Sometimes you need to convert between \( m/s \) and \( km/h \).
To go from \( km/h \) to \( m/s \): Divide by 3.6.
To go from \( m/s \) to \( km/h \): Multiply by 3.6.

Quick Review Box:
- Speed is Scalar.
- Velocity is Vector (Speed in a given direction).
- Unit is always meters per second (\( m/s \)).


3. Acceleration: Changing it up

Acceleration is how quickly your velocity is changing. If you speed up, slow down, or even just change direction, you are accelerating!

The formula for acceleration is:

\( \text{acceleration (m/s}^2\text{)} = \frac{\text{change in speed (m/s)}}{\text{time taken (s)}} \)

Or in symbols: \( a = \frac{\Delta v}{t} \)

Did you know? When an object falls through the air (in "free fall"), it accelerates at roughly \( 10 \, m/s^2 \) because of gravity. This means every second it falls, it gets \( 10 \, m/s \) faster!


4. The "Big" Equation of Motion

Sometimes you don't know the time it took for something to move, but you know the distance. In those cases, we use this special relationship:

\( (\text{final speed})^2 - (\text{initial speed})^2 = 2 \times \text{acceleration} \times \text{distance} \)

Symbols: \( v^2 - u^2 = 2as \)

Example: A car accelerates from \( 0 \, m/s \) to \( 20 \, m/s \) with an acceleration of \( 2 \, m/s^2 \). How far did it travel?
1. \( v = 20 \), \( u = 0 \), \( a = 2 \).
2. \( 20^2 - 0^2 = 2 \times 2 \times s \)
3. \( 400 = 4s \)
4. \( s = 100 \, m \)

Key Takeaway: Acceleration is about the rate of change. A high acceleration means you are reaching a high speed very quickly.


5. Motion Stories: Distance-Time and Velocity-Time Graphs

Graphs are a great way to "see" motion. There are two main types you need to master:

A. Distance-Time Graphs
  • The Slope (Gradient): Represents the speed.
    - Steeper line = Faster speed.
    - Flat horizontal line = Stationary (stopped).
    - Curved line = Changing speed (acceleration).
B. Velocity-Time Graphs
  • The Slope (Gradient): Represents the acceleration.
    - Steeper line = Greater acceleration.
    - Flat horizontal line = Constant speed (NOT stopped!).
    - Sloping downwards = Deceleration (slowing down).
  • The Area Under the Line: Represents the distance travelled.

Analogy: Think of a Velocity-Time graph like a car's speedometer. If the needle stays at 50, the line is flat, but the car is still moving!

Common Mistake to Avoid: On a Distance-Time graph, a flat line means you aren't moving. On a Velocity-Time graph, a flat line means you are moving at a steady speed. Always check the labels on the axes first!


6. Practical Physics: Measuring Motion

In the lab, we often investigate motion using a trolley and a ramp. There are two main ways to measure speed and acceleration:

  1. Stopwatches and Rulers: Simple but prone to "human reaction time" errors.
  2. Light Gates: These are much more accurate. A light gate sends a beam of light across the track. When the trolley passes through, it breaks the beam. A computer measures exactly how long the beam was broken for to calculate the speed instantly.

Step-by-Step: Investigating a Trolley
1. Set up a ramp at an angle.
2. Place a light gate at the top and one at the bottom.
3. Measure the distance between the gates.
4. Let the trolley go! The computer will record the time and calculate acceleration for you.

Key Takeaway: Light gates remove human error, making your results for speed and acceleration more precise and accurate.


Quick Summary Review:
- Scalars have size only; Vectors have size and direction.
- Average speed = Distance / Time.
- Acceleration = Change in speed / Time.
- Distance-Time graph slope = Speed.
- Velocity-Time graph slope = Acceleration; Area = Distance.