🚗 Chapter 1.2: Motion – Ready to Roll!

Hello future Physicists! This chapter is all about describing how things move. Whether you're watching a car race, catching a ball, or planning a trip, understanding motion is fundamental to physics. Don't worry if the graphs seem tricky at first—we'll break them down step-by-step using clear examples!

1. Describing Movement: Speed and Velocity (Core & Supplement)

When we talk about movement, we need ways to measure it accurately. The first concepts are speed and velocity.

Key Concept 1: Speed

Speed tells us how fast an object is moving. It is defined as the distance travelled per unit time.

  • Unit: Metres per second (\(m/s\)) or kilometres per hour (\(km/h\)).
  • Formula:
    $$\text{Speed} = \frac{\text{Distance travelled}}{\text{Time taken}}$$ $$v = \frac{S}{t}$$

Example: If a sprinter covers 100 metres (\(S\)) in 10 seconds (\(t\)), their speed is \(100 \text{ m} / 10 \text{ s} = 10\text{ m/s}\).

Calculating Average Speed

When an object starts and stops, or speeds up and slows down, its speed is changing. The average speed gives us an overall idea of the journey.

  • Definition: The total distance travelled divided by the total time taken.
  • Formula:
    $$\text{Average speed} = \frac{\text{Total distance travelled}}{\text{Total time taken}}$$
Key Concept 2: The Vector Difference (Speed vs. Velocity)

This is a crucial distinction, linked to the "Physical Quantities" section (1.1):

  • Speed is a scalar quantity: It only has magnitude (size).
    (e.g., The car is moving at 50 km/h.)
  • Velocity is a vector quantity: It has both magnitude and direction.
    (e.g., The car is moving at 50 km/h East.)

Definition of Velocity: Velocity is the speed in a given direction.

Quick Review: Speed vs. Velocity

If you run a lap on a circular track and end up where you started, your average speed is high, but your average velocity is zero (because your direction changed and your total displacement is zero!).

2. Acceleration and Deceleration (Supplement)

When an object’s velocity changes (either its speed or its direction), it is accelerating.

Definition of Acceleration

Acceleration is defined as the change in velocity per unit time.

  • Unit: Metres per second squared (\(m/s^2\)).
  • Formula:
    $$\text{Acceleration} = \frac{\text{Change in velocity}}{\text{Time taken}}$$ $$a = \frac{\Delta v}{\Delta t}$$

Note: The Greek letter Delta (\(\Delta\)) just means "change in". So \(\Delta v\) means the final velocity minus the initial velocity: \(v - u\).

Understanding Deceleration (Negative Acceleration)

When an object slows down, its velocity is decreasing. This is called deceleration.

In physics calculations, deceleration is simply treated as a negative acceleration. If a car slows from 20 m/s to 10 m/s, the change in velocity is negative, giving a negative acceleration value.

Common Mistake to Avoid: Deceleration does not mean acceleration in the opposite direction; it simply means slowing down (negative change in velocity).

3. Visualising Motion: Graphs (Core & Supplement)

Graphs are the most common way we analyse motion. We focus on two types: Distance-Time and Speed-Time graphs.

3.1 Distance-Time Graphs (D-T Graphs)

These graphs plot the total distance covered (y-axis) against the time elapsed (x-axis).

Interpreting D-T Graph Shapes (Qualitatively)
  • Horizontal Line: Distance is not changing over time. The object is at rest (\(v=0\)).
  • Straight Line sloping up: Distance is changing uniformly. The object is moving with constant speed.
  • Curve sloping up (getting steeper): The speed is increasing. The object is accelerating.
  • Curve sloping up (getting less steep): The speed is decreasing. The object is decelerating.
Calculating Speed from a D-T Graph

For a straight-line section of a D-T graph, the speed is calculated by finding the gradient (slope) of the line.

$$ \text{Speed} = \text{Gradient} = \frac{\text{Change in Distance}}{\text{Change in Time}} $$

Don't worry if this seems tricky at first! Remember the gradient is just "rise over run". Pick two clear points on the straight line, measure the distance difference (rise) and the time difference (run), and divide them.

3.2 Speed-Time Graphs (S-T Graphs)

These graphs plot the speed (or velocity) of an object (y-axis) against the time elapsed (x-axis).

Interpreting S-T Graph Shapes (Qualitatively)
  • Horizontal Line: Speed is constant. The object is moving at constant speed (\(a=0\)).
  • Straight Line sloping up: Speed is increasing uniformly. The object is moving with constant acceleration. (This is key for Supplement: *constant acceleration*).
  • Straight Line sloping down: Speed is decreasing uniformly. The object is decelerating (constant negative acceleration).
  • Curved Line (Supplement): The acceleration is changing (it is changing acceleration).
Calculating Acceleration from an S-T Graph (Supplement)

For a straight-line section of an S-T graph, the acceleration is calculated by finding the gradient of the line.

$$ \text{Acceleration} = \text{Gradient} = \frac{\text{Change in Speed}}{\text{Change in Time}} $$

Calculating Distance from an S-T Graph (Core & Supplement)

The total distance travelled by the object is found by calculating the area under the speed-time graph.

If the graph section is a straight line (constant speed or constant acceleration), the area will be a simple shape like a rectangle (constant speed) or a trapezium/triangle (constant acceleration).

Memory Aid:

  • D-T Graph: Gradient gives Speed.
  • S-T Graph: Gradient gives Acceleration; Area gives Distance. (SAD!)
Did you know?

Calculating the area under a curve is typically done using calculus, but for IGCSE, we stick to motion with constant acceleration, which means the graphs are straight lines and you can use simple area formulas (triangles and rectangles)!

4. The Physics of Falling: Gravity and Resistance (Core & Supplement)

4.1 Acceleration of Free Fall (\(g\)) (Core)

When an object falls solely under the influence of gravity (ignoring air resistance), it experiences free fall.

  • Value: The acceleration of free fall, \(g\), is approximately constant near the surface of the Earth.
  • Magnitude: \(g \approx 9.8 \text{ m/s}^2\).

This means that for every second an object is falling freely, its velocity increases by 9.8 m/s.

4.2 Falling with Resistance and Terminal Velocity (Supplement)

In the real world, objects falling through air (a gas) or liquid experience a frictional force called drag (or air resistance).

Here is a step-by-step description of a skydiver falling (or any object falling with resistance):

  1. Start of Motion: The object accelerates rapidly because the only force acting is weight (gravity) pulling it down. Drag (air resistance) is zero.
  2. Speed Increases, Drag Increases: As the object speeds up, the air resistance acting upwards increases. The resultant force (Weight - Drag) decreases, so the acceleration decreases (Newton's Second Law: \(F=ma\)).
  3. Reaching Terminal Velocity: Eventually, the air resistance force becomes exactly equal to the object’s weight.
    • The resultant force is zero.
    • Since \(F=0\), the acceleration is zero.
    • The object continues to fall at a maximum constant velocity. This velocity is called the terminal velocity.

For a skydiver, once the parachute opens, the surface area increases dramatically, causing a huge increase in drag. This causes rapid deceleration until a new, much lower terminal velocity is reached, allowing for a safe landing.

Key Takeaway for Motion

Motion is described using scalars (like speed and distance) and vectors (like velocity and acceleration). Graphs are essential tools: the gradient tells you the rate of change (speed or acceleration), and the area under a speed-time graph gives the distance. In real-world falling, air resistance causes acceleration to drop to zero, resulting in a maximum constant speed called terminal velocity.