Motion | IGCSE Physics Revision Notes

1. Overview

Motion is the study of how objects move through space and time. Understanding motion allows us to predict where an object will be in the future and how forces like gravity and air resistance affect its travel, which is essential for everything from road safety to space exploration.

Key Definitions

Speed: The distance travelled per unit time (a scalar quantity).
Velocity: The speed of an object in a specific direction (a vector quantity).
Distance: The total length of the path travelled by an object.
Acceleration: The rate of change of velocity per unit time.
Gradient: The steepness of a slope on a graph, calculated as "rise over run."
Terminal Velocity: The constant maximum velocity reached by a falling object when the upward force of resistance equals the downward force of weight.

Core Content

Speed and Velocity

Speed tells us how fast an object is moving, while velocity includes the direction.

Speed Equation: $v = \frac{d}{t}$
Average Speed: When an object changes speed during a journey, we calculate the average by dividing the total distance by the total time taken.

Distance-Time (D-T) Graphs

These graphs show how far an object has moved from a starting point over time.

At Rest: A horizontal flat line (distance is not changing).
Constant Speed: A straight diagonal line.
Acceleration: The line curves upwards (getting steeper).
Deceleration: The line curves downwards (getting flatter).
Calculating Speed: The gradient (slope) of a straight-line section equals the speed.

A graph with Distance on the Y-axis and Time on the X-axis. Shows a flat line (stationary), a straig — A graph with Distance on the Y-axis and Time on the X-axis. Shows a flat line (s...

Speed-Time (S-T) Graphs

These graphs show how the speed of an object changes over time.

At Rest: A horizontal line on the x-axis (speed = 0).
Constant Speed: A horizontal line above the x-axis.
Acceleration: A line sloping upwards.
Deceleration: A line sloping downwards.
Calculating Distance: The area under the line of a speed-time graph represents the total distance travelled.

A graph with Speed on the Y-axis and Time on the X-axis. A rectangle area represents constant speed; — A graph with Speed on the Y-axis and Time on the X-axis. A rectangle area repres...

Free Fall

Near the Earth's surface, all objects fall with the same constant acceleration if we ignore air resistance. This is called the acceleration of free fall ($g$).

Value of $g$: approximately $9.8\text{ m/s}^2$.

Worked Example (Core): A car travels 150 meters in 10 seconds. Calculate its speed.

$v = \frac{d}{t}$
$v = \frac{150}{10} = 15\text{ m/s}$

Extended Content (Extended Curriculum Only)

Acceleration

Acceleration is the change in velocity per unit time.

Equation: $a = \frac{\Delta v}{t}$ (where $\Delta v$ is the change in velocity: $final - initial$).
Deceleration: This is simply negative acceleration. If an object slows down, its acceleration value will be negative (e.g., $-2\text{ m/s}^2$).

Speed-Time Graphs (Advanced)

Gradient: The gradient of a speed-time graph represents the acceleration.
Constant Acceleration: A straight diagonal line.
Changing Acceleration: A curved line. If the curve gets steeper, acceleration is increasing; if it levels off, acceleration is decreasing.

Falling Objects and Terminal Velocity

When an object falls in a uniform gravitational field:

Initial Fall: The only force is Weight. The object accelerates at $g$ ($9.8\text{ m/s}^2$).
Increasing Speed: As speed increases, Air Resistance (drag) increases. This reduces the resultant force, so acceleration decreases.
Terminal Velocity: Eventually, Air Resistance increases until it equals the Weight. The forces are balanced (resultant force = 0). The object stops accelerating and falls at a constant terminal velocity.

Worked Example (Extended): A sprinter accelerates from $0\text{ m/s}$ to $12\text{ m/s}$ in $3$ seconds. Calculate the acceleration.

$a = \frac{(v - u)}{t}$
$a = \frac{(12 - 0)}{3} = 4\text{ m/s}^2$

Key Equations

Concept	Equation	Symbols & Units
Speed	$v = \frac{d}{t}$	$v = \text{speed (m/s)}, d = \text{distance (m)}, t = \text{time (s)}$
Avg. Speed	$v_{avg} = \frac{\text{Total } d}{\text{Total } t}$	Units: $\text{m/s}$
Acceleration	$a = \frac{(v - u)}{t}$	$a = \text{accel (m/s}^2), v = \text{final vel, } u = \text{initial vel, } t = \text{time}$

Common Mistakes to Avoid

❌ Wrong: Saying a scalar (like speed) has a direction.
- ✓ Right: Speed is just a magnitude; only vectors (like velocity) have direction.
❌ Wrong: Believing an object's weight affects how hard it is to move it horizontally (inertia).
- ✓ Right: Mass—not weight—determines resistance to acceleration (inertia). Weight is a vertical force due to gravity.
❌ Wrong: Confusing Distance-Time graphs with Speed-Time graphs.
- ✓ Right: Always check the Y-axis label. A flat line means "stopped" on a D-T graph, but "constant speed" on an S-T graph.

Exam Tips

Show Your Units: Always include $\text{m/s}$ for speed and $\text{m/s}^2$ for acceleration. You can lose easy marks by forgetting them.
The "Area" Trick: In any exam question asking for distance from a speed-time graph, immediately look for shapes (rectangles and triangles) under the line and calculate their area.
Gradient Calculation: When calculating the gradient, use as much of the line as possible (draw a large triangle) to improve accuracy.