CORE Physics (9223) | Motion

🚀 Motion: Understanding How Things Move

Welcome to the chapter on Motion! This is the foundation of all physics, helping us understand how things get from point A to point B. Since this chapter is part of the "Forces and their effects" section, mastering motion is crucial—because forces are what cause motion to change!

Don't worry if you find the graphs tricky; we will break everything down into easy steps. By the end of these notes, you’ll be able to calculate how fast an object is moving and describe exactly how its movement changes over time. Let’s get started!

1. Describing Where You Are: Scalars and Vectors

In physics, we need precise language. Some measurements only care about the size (or magnitude), while others care about the size and the direction.

Key Definitions: Scalar vs. Vector

• Scalar Quantity: This only has magnitude (size).
  Examples: Distance, Speed, Mass, Time.
• Vector Quantity: This has both magnitude (size) AND direction.
  Examples: Displacement, Velocity, Acceleration, Force.

🔥 Memory Aid: Think of a 'V' for Vector, which stands for Very specific (it needs direction!).

Distance vs. Displacement (The Pizza Analogy)

These two terms sound similar but are crucial vectors and scalars:

Imagine you leave your house, walk 50 metres east, and then walk 50 metres west, ending up exactly where you started.

• Distance (Scalar): The total path travelled.
  In the example: 50 m + 50 m = 100 m.
• Displacement (Vector): The straight-line distance from the start point to the end point, including direction.
  In the example: Since you finished where you started, your displacement is 0 m.

Did you know? If a delivery driver has a displacement of 0 m, they got lost and ended up back at the restaurant, even if they drove 100 km!

Speed vs. Velocity

Just like Distance and Displacement, Speed and Velocity are related:

• Speed (Scalar): How fast an object is moving (Distance ÷ Time). It doesn't care about direction.
• Velocity (Vector): How fast an object is moving in a specific direction (Displacement ÷ Time).

Key Takeaway: If a car drives around a roundabout at a constant 30 km/h, its speed is constant, but its velocity is constantly changing because its direction is changing.

2. Calculating Speed

Speed tells us the rate at which distance is covered.

The Formula for Speed

The standard international (SI) unit for distance is metres (m), and for time is seconds (s). Therefore, the standard unit for speed is metres per second (\(m/s\)).

$$ \text{Speed} = \frac{\text{Distance travelled}}{\text{Time taken}} $$

Or, using symbols: $$ v = \frac{d}{t} $$

Where: \(v\) = speed/velocity, \(d\) = distance/displacement, \(t\) = time.

Average Speed vs. Instantaneous Speed

When you calculate speed using the formula above, you usually find the average speed for the entire journey.

• Average Speed: Total distance divided by total time. (Used when calculating a whole trip).
• Instantaneous Speed: The speed at one exact moment in time. (What your car speedometer shows you right now).

3. Understanding Acceleration

If an object's velocity is changing—either speeding up, slowing down, or changing direction—it is accelerating. Acceleration is the rate at which velocity changes.

Calculating Acceleration

We calculate acceleration by finding the change in velocity (\(v - u\)) and dividing it by the time it took for that change.

$$ \text{Acceleration} = \frac{\text{Change in velocity}}{\text{Time taken}} = \frac{\text{Final velocity} - \text{Initial velocity}}{\text{Time taken}} $$

Or, using symbols: $$ a = \frac{v - u}{t} $$

• \(a\) = acceleration (\(m/s^2\))
• \(v\) = final velocity (\(m/s\))
• \(u\) = initial velocity (\(m/s\))
• \(t\) = time taken (\(s\))

Units of Acceleration

The standard unit for acceleration is metres per second squared (\(m/s^2\)). This might sound strange, but it just means 'metres per second, per second'—the velocity (m/s) changes every second.

Deceleration (Slowing Down)

When an object slows down, we call this deceleration. In physics, deceleration is simply negative acceleration. If your calculation results in a negative value for \(a\), it means the object is slowing down.

Key Takeaway: Acceleration is caused by a net force acting on an object. This is why motion is key to understanding forces!

4. Visualising Motion: Graphs

Graphs are essential tools in physics because they show the entire journey at a glance. We primarily use two types of motion graphs: Distance-Time and Speed-Time.

4.1. Distance-Time Graphs (DTG)

These graphs plot Distance (Y-axis) against Time (X-axis).

The Golden Rule for DTGs: The gradient (slope) of a Distance-Time graph represents the Speed.

Interpreting the Slope:

• Zero Gradient (Horizontal Line): The distance is not changing over time. The object is stationary (stopped). Speed = 0.
• Constant Positive Gradient (Straight Diagonal Line): The object is covering the same distance every second. It is moving at constant speed.
• Increasing Gradient (Curving upwards): The object is covering more distance every second. It is accelerating (speeding up).
• Steeper Slope: Means a faster speed.

4.2. Speed-Time Graphs (STG)

These graphs plot Speed (Y-axis) against Time (X-axis). These are crucial for calculating acceleration and total distance travelled.

The Golden Rules for STGs:

1. The Gradient (Slope) represents Acceleration.
2. The Area under the graph represents the Distance travelled.

Interpreting the Speed-Time Graph:

• Zero Gradient (Horizontal Line): Speed is not changing. The acceleration is zero. The object is moving at constant velocity.
• Constant Positive Gradient (Straight Line up): The speed is increasing steadily. The object is experiencing constant positive acceleration.
• Constant Negative Gradient (Straight Line down): The speed is decreasing steadily. The object is decelerating (constant negative acceleration).
• Line on the X-axis (Speed = 0): The object is stationary.

📌 Important Skill: Calculating Distance from an STG
To find the distance, you calculate the area of the shape under the line. Often, this area is a simple rectangle, triangle, or a combination of both (a trapezium).

Example: If the motion forms a rectangle (constant speed), Area = speed × time.
Example: If the motion forms a triangle (constant acceleration from rest), Area = ½ × base × height.