Physics (9203) | Motion

👋 Welcome to the World of Motion!

Hello future Physicist! Motion is one of the most fundamental topics in Physics. It’s how we describe everything from a snail crawling to a rocket launching. Don't worry if this chapter seems tricky at first; we will break down complex ideas like acceleration and graphs into simple, digestible steps. By the end, you'll be able to read the story of any moving object just by looking at a line on a graph!

This chapter is the foundation for understanding Forces and their Effects, as forces are what cause motion to change. Let's get moving!

📐 Section 1: Describing Movement – Speed and Velocity

Understanding Distance and Displacement

Before we talk about how fast something is moving, we need to know what it means to move.

• Distance: This is how far an object has travelled in total. It doesn't matter what direction you went.
  Example: If you walk 5m forward and 5m back, your distance travelled is 10m.
• Displacement: This is the shortest distance from the starting point to the finishing point, and it must include direction.
  Example: If you walk 5m forward and 5m back, your displacement is 0m (you ended up where you started).

Quick Tip: Distance is measured in metres (m) or kilometres (km).

Speed vs. Velocity: A Crucial Difference

In everyday life, we use speed and velocity interchangeably, but in Physics, they mean different things. This difference comes down to whether we care about direction.

Key Definitions: Scalar vs. Vector

• Scalar Quantity: A quantity that only has magnitude (size). Examples: Speed, Distance, Time, Mass.
• Vector Quantity: A quantity that has both magnitude (size) and direction. Examples: Velocity, Displacement, Force.

1. Speed

Speed is defined as the rate at which distance is covered. It is a scalar quantity.

The standard unit for speed is metres per second (m/s), although kilometres per hour (km/h) is also common.

The formula for average speed is:

\( \text{Average Speed} = \frac{\text{Distance travelled}}{\text{Time taken}} \)

2. Velocity

Velocity is defined as the rate of change of displacement. It is a vector quantity, meaning it must include a direction.

🚀 Section 2: Acceleration – The Change in Motion

What is Acceleration?

If an object’s velocity changes—either by speeding up, slowing down, or changing direction—we say the object is accelerating.

Acceleration (a) is defined as the rate of change of velocity. Since velocity is a vector, acceleration is also a vector quantity.

Calculating Acceleration

To calculate acceleration, we need to know the change in velocity (\( \Delta v \)) and the time taken (\( t \)).

We use the following symbols:

• \(u\): Initial velocity (starting velocity)
• \(v\): Final velocity (ending velocity)
• \(t\): Time taken

The formula for acceleration is:

\( a = \frac{\text{Change in velocity}}{\text{Time taken}} = \frac{(v - u)}{t} \)

The standard unit for acceleration is metres per second squared (\( \text{m/s}^2 \)).

Step-by-Step Calculation Example

Example: A cyclist starts from rest and reaches a velocity of 10 m/s in 5 seconds. What is their acceleration?

1. Identify variables: Start from rest means \(u = 0 \text{ m/s}\). Final velocity \(v = 10 \text{ m/s}\). Time \(t = 5 \text{ s}\).
2. Apply the formula: \( a = \frac{(v - u)}{t} \)
3. Calculate: \( a = \frac{(10 - 0)}{5} = \frac{10}{5} = 2 \)
4. State the result and unit: The acceleration is \( 2 \text{ m/s}^2 \).

Deceleration (Negative Acceleration)

When an object slows down, its final velocity (\( v \)) is less than its initial velocity (\( u \)). This results in a negative value for acceleration.

Don’t Panic!
If you calculate a negative acceleration, it simply means the object is decelerating (slowing down).

📈 Section 3: The Visual Story – Graphs of Motion

Graphs are essential tools in physics because they allow us to see how motion changes over time, without complex calculations. You need to be able to interpret two main types of graphs.

3a: Distance-Time Graphs

These graphs plot distance (on the y-axis) against time (on the x-axis).

Interpreting the Gradient (Slope)

On a Distance-Time graph, the gradient (steepness of the line) represents the speed.

\( \text{Gradient} = \frac{\text{Change in y}}{\text{Change in x}} = \frac{\text{Distance}}{\text{Time}} = \text{Speed} \)

Reading Distance-Time Graph Shapes

• Horizontal Line (Flat Line): The distance is not changing over time. This means the object is stationary (speed = 0).
• Straight Line with Constant Positive Slope: The object covers the same distance in the same time interval. This means constant speed.
• Steeper Slope: The object is covering more distance in the same time. This means faster constant speed.
• Curved Line (Getting steeper): The speed is increasing. The object is accelerating.

3b: Velocity-Time Graphs

These graphs plot velocity (on the y-axis) against time (on the x-axis). They give us even more information than distance-time graphs.

Interpreting the Velocity-Time Graph

There are two crucial pieces of information you can get from a Velocity-Time graph:

1. The Gradient (Slope) = Acceleration

On a Velocity-Time graph, the gradient represents the acceleration.

\( \text{Gradient} = \frac{\text{Change in y}}{\text{Change in x}} = \frac{\text{Change in Velocity}}{\text{Time}} = \text{Acceleration} \)

• Horizontal Line (Flat Line): Velocity is constant. The object is moving at a steady speed, so acceleration is zero.
• Straight Line with Positive Slope: Velocity is increasing steadily. This is constant positive acceleration. (Speeding up).
• Straight Line with Negative Slope (Going Down): Velocity is decreasing steadily. This is constant negative acceleration / deceleration. (Slowing down).

2. The Area Under the Graph = Distance Travelled

This is a very important concept. The area under a velocity-time graph equals the total distance travelled by the object during that time.

Step-by-Step Calculation: Finding Distance

1. Identify the Area Shape: The area under the line will usually be a simple shape: a rectangle, a triangle, or a trapezium (a combination of a rectangle and a triangle).
2. Use Geometry Formulas:
   • Area of Rectangle = length \(\times\) width
   • Area of Triangle = \(\frac{1}{2}\) \(\times\) base \(\times\) height
3. Calculate: Sum up the areas of the shapes to find the total distance.

Example: If the graph forms a triangle with a base of 10s and a height (velocity) of 20 m/s, the distance travelled is: \( \frac{1}{2} \times 10 \times 20 = 100 \text{ metres} \).

📝 Final Review of Motion Concepts

You have successfully covered the core concepts of motion! Remember that motion is the study of how things move, and the concepts of speed, velocity, and acceleration are the tools we use to describe that movement precisely.

• Speed is a scalar (no direction); Velocity is a vector (includes direction).
• Acceleration is the change in velocity over time.
• The standard unit for speed/velocity is \( \text{m/s} \).
• The standard unit for acceleration is \( \text{m/s}^2 \).
• When reading graphs, pay close attention to the labels on the axes (Distance or Velocity) to correctly interpret the slope!

You got this! Now try practising interpreting those motion graphs!