👋 Welcome to Movement and Position!
Hey there, future Physicist! This chapter is all about describing how things move. Whether you’re walking to school, riding a bike, or watching a formula car zoom past, the concepts of movement and position are the fundamental building blocks of all physics. Don't worry if this seems tricky at first—we're going to break down these concepts using clear steps and real-world examples!
Ready to learn how to precisely describe speed, distance, and acceleration? Let's dive in!
1. Defining Movement: Scalars vs. Vectors
Before we measure movement, we must understand the difference between quantities that only care about how much and quantities that also care about where to.
1.1 Scalars (Magnitude Only)
A scalar quantity is one that is fully described by its size or magnitude (a number and a unit). Direction does not matter.
- Examples: Distance, Time, Mass, Energy, Speed.
1.2 Vectors (Magnitude and Direction)
A vector quantity is one that requires both magnitude and a specific direction to be fully described.
- Examples: Displacement, Force, Momentum, Velocity, Acceleration.
💡 Memory Aid: Think of a Vector as needing a "V-ery specific Direction."
1.3 Distance vs. Displacement
These two terms are often confused, but they mean very different things in Physics.
| Concept | Definition | Type |
| Distance (d) | The total length of the path travelled. | Scalar |
| Displacement (s) | The shortest straight-line distance from the starting point to the finishing point, including the direction. | Vector |
Example: Imagine you walk 3 km East, and then turn around and walk 3 km West back to where you started.
- Your Distance travelled is 3 km + 3 km = 6 km.
- Your Displacement is 0 km (because your starting and ending positions are the same).
🔑 Key Takeaway: Movement quantities are either Scalars (just size) or Vectors (size and direction). Displacement is the vector version of distance.
2. Describing Rate: Speed and Velocity
Now that we know the difference between distance and displacement, we can look at the rate at which they change.
2.1 Speed (Scalar)
Speed is defined as the rate of change of distance. It tells you how fast an object is moving, regardless of the direction.
Formula:
$$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $$The standard unit for speed is metres per second (m/s), though kilometres per hour (km/h) is often used in everyday life.
2.2 Velocity (Vector)
Velocity is defined as the rate of change of displacement. It is speed in a specific direction.
Formula:
$$ \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} $$Did You Know? If you are driving in a perfect circle at a constant speed, your speed is constant, but your velocity is constantly changing because your direction is changing!
2.3 Calculating Average Speed
Most objects don't travel at a perfect, constant speed. Therefore, we often calculate average speed over the entire journey.
$$ \text{Average Speed} = \frac{\text{Total Distance Travelled}}{\text{Total Time Taken}} $$🚨 Common Mistake Alert: When calculating speed, always ensure your units are consistent! If distance is in metres (m), time must be in seconds (s) to get m/s.
A runner covers a distance of 400 metres in 50 seconds.
$$ \text{Speed} = \frac{400 \text{ m}}{50 \text{ s}} = 8 \text{ m/s} $$
🔑 Key Takeaway: Speed is a scalar describing distance over time. Velocity is a vector describing displacement over time (speed plus direction).
3. Changing Velocity: Acceleration
What happens when you press the accelerator pedal in a car? You are causing a change in velocity. This change is called acceleration.
3.1 Defining Acceleration (Vector)
Acceleration (\(a\)) is the rate of change of velocity.
Because velocity is a vector, acceleration is also a vector.
An object accelerates if it:
- Speeds up (positive acceleration).
- Slows down (negative acceleration, also called deceleration or retardation).
- Changes direction (even if its speed remains constant).
3.2 The Acceleration Formula
We calculate acceleration by finding the change in velocity (\(\Delta v\)) and dividing it by the time taken (\(t\)).
We use the following symbols:
- \(u\): Initial velocity (starting velocity)
- \(v\): Final velocity
- \(t\): Time taken
The standard unit for acceleration is metres per second squared (\( \text{m/s}^2 \)).
Example: An object starts at rest (\(u = 0 \text{ m/s}\)) and accelerates to \(20 \text{ m/s}\) in \(4 \text{ s}\).
$$ a = \frac{20 \text{ m/s} - 0 \text{ m/s}}{4 \text{ s}} = 5 \text{ m/s}^2 $$3.3 Constant Acceleration and Gravity
One very important example of constant acceleration is free fall near the Earth's surface.
- Ignoring air resistance, all objects fall with the same constant acceleration due to gravity, often denoted as \(g\).
- For calculations in IGCSE, you may be asked to use the value \(g \approx 9.8 \text{ m/s}^2\) or simplified to \(10 \text{ m/s}^2\).
🔑 Key Takeaway: Acceleration measures how quickly velocity changes. It is calculated by (Final Velocity - Initial Velocity) / Time. Deceleration is just negative acceleration.
4. Visualizing Movement: Graphs
Graphs are essential tools in Physics because they allow us to see patterns and easily calculate speed, acceleration, and distance travelled.
4.1 Distance-Time Graphs (Calculating Speed)
In a Distance-Time graph:
- The Y-axis shows Distance (or Displacement).
- The X-axis shows Time.
The most important feature of this graph is the gradient (steepness).
$$ \text{Gradient} = \frac{\text{Change in Y}}{\text{Change in X}} = \frac{\text{Distance}}{\text{Time}} $$
Therefore, the gradient of a distance-time graph represents the speed.
Interpreting the Shapes:
- Horizontal Line (Gradient = 0): The object is stopped (stationary).
- Straight Diagonal Line (Constant Gradient): The object is moving at a constant speed.
- Steeper Gradient: Faster constant speed.
- Curving Line (getting steeper): The object is accelerating (speeding up).
4.2 Speed/Velocity-Time Graphs (Calculating Acceleration and Distance)
Velocity-Time graphs are powerful because they give us two key pieces of information from one graph.
In a Velocity-Time graph:
- The Y-axis shows Velocity (or Speed).
- The X-axis shows Time.
A. Acceleration (The Gradient)
$$ \text{Gradient} = \frac{\text{Change in Y}}{\text{Change in X}} = \frac{\text{Change in Velocity}}{\text{Time}} $$
Therefore, the gradient of a velocity-time graph represents the acceleration.
- Horizontal Line (Gradient = 0): Zero acceleration (constant velocity).
- Positive Gradient (Sloping up): Positive acceleration (speeding up).
- Negative Gradient (Sloping down): Deceleration (slowing down).
B. Distance Travelled (The Area Under the Graph)
The total distance travelled by the object is represented by the area underneath the velocity-time graph.
Step-by-Step Calculation for Distance:
- Identify the shape under the line (usually rectangles and triangles).
- Calculate the area of each shape.
- Add the areas together to find the total distance.
- Area of Rectangle = length × width
- Area of Triangle = 0.5 × base × height
🔑 Key Takeaway: On a distance-time graph, the gradient is Speed. On a velocity-time graph, the gradient is Acceleration, and the area under the graph is Distance travelled.