Scalars, vectors and motion graphs

Q: What is the formula for calculating average speed?

\(\text{distance travelled} = ext{average speed} imes ext{time}\)

Physics (1PH0) · Pearson Edexcel GCSE (9-1) · 4 min read · Updated: 7 Sept 2026

Introduction to Motion

Welcome to the study of how things move! Whether it's a car racing down a track or a leaf falling from a tree, Physics uses specific tools to describe motion. In this chapter, we will learn how to distinguish between different types of measurements and how to use graphs to tell the story of an object's journey. Mastering these basics is the first step toward understanding the "Motion and Forces" section of your Paper 1 exam.

1. Scalars and Vectors

In Physics, every measurement we take falls into one of two categories: scalars or vectors. The difference is all about direction.

What is a Scalar?

A scalar quantity has magnitude (size) only. It tells you "how much," but it doesn't care which way you are going.
Examples: Distance, speed, mass, time, and energy.

What is a Vector?

A vector quantity has both magnitude (size) AND direction.
Examples: Displacement, velocity, acceleration, force, weight, and momentum.

Distance vs. Displacement

These two are often confused, but they are very different in Physics:
- Distance (Scalar): How far an object has travelled in total (e.g., "I walked 500 metres").
- Displacement (Vector): How far an object is from its starting point, in a straight line, including the direction (e.g., "I am 200 metres North of my house").

Quick Tip: Use the "First Letter" trick to remember them!
- Scalar = Size (magnitude) only.
- Vector = Very specific direction.

2. Speed and Velocity

Just like distance and displacement, speed and velocity are a pair. Speed is a scalar, and velocity is a vector.

Calculating Average Speed

To find the average speed of an object, use this formula:
\(\text{distance travelled} = \text{average speed} \times \text{time}\)

Typical Everyday Speeds:
You should be able to estimate these typical speeds for the exam:
- Walking: \(\approx 1.5 \text{ m/s}\)
- Running: \(\approx 3 \text{ m/s}\)
- Cycling: \(\approx 6 \text{ m/s}\)
- Speed of sound in air: \(\approx 330 \text{ m/s}\)

3. Acceleration

Acceleration is the rate at which velocity changes. Because it involves velocity, acceleration is a vector. An object is accelerating if it speeds up, slows down (deceleration), or changes direction.

The Acceleration Formula

To calculate acceleration (\(a\)), you need the initial velocity (\(u\)), the final velocity (\(v\)), and the time taken (\(t\)):
\(a = \frac{v - u}{t}\)
Units: Acceleration is measured in metres per second squared (\(\text{m/s}^2\)).

Acceleration due to Gravity

When an object is in free fall (falling with only gravity acting on it), it accelerates at a constant rate. For your Edexcel exams, this value is:
\(g = 10 \text{ m/s}^2\)

The "v squared" Equation

Sometimes you need to calculate acceleration or distance without knowing the time. For this, we use the following equation (provided on your formula sheet):
\(v^2 - u^2 = 2 \times a \times x\)
- \(v\) = final velocity (\(\text{m/s}\))
- \(u\) = initial velocity (\(\text{m/s}\))
- \(a\) = acceleration (\(\text{m/s}^2\))
- \(x\) = distance (\(\text{m}\))

4. Distance-Time Graphs

A distance-time graph shows how far an object has travelled over time.

The Gradient (Slope): Represents the speed of the object.
A Steeper Slope: Means the object is moving faster.
A Horizontal (Flat) Line: Means the object is stationary (not moving).
A Curve: Means the speed is changing (acceleration).

5. Velocity-Time Graphs

A velocity-time graph tells a much more detailed story about an object's motion.

Reading the Graph

The Gradient (Slope): Represents the acceleration.
A Horizontal (Flat) Line: Means the object is moving at a constant velocity.
A Sloping Line Upwards: Means the object is accelerating.
A Sloping Line Downwards: Means the object is decelerating.

The Area Under the Graph

One of the most important skills is calculating the area under a velocity-time graph. This area is equal to the distance travelled.
- For a rectangle: \(\text{area} = \text{base} \times \text{height}\)
- For a triangle: \(\text{area} = 0.5 \times \text{base} \times \text{height}\)
- For Higher Tier: If the graph is a curve, you may need to estimate the area by counting squares beneath the line.

6. Laboratory Methods

In a school lab, we can't always rely on a stopwatch because human reaction time causes errors. To measure speed and acceleration accurately, we use:

Light Gates: These are connected to a computer. When an object passes through the beam, the computer records the time precisely.
Trolleys and Ramps: By measuring the distance between two light gates and the time taken for a trolley to pass between them, the computer calculates the velocity.

Chapter Summary Checklist

Key Takeaways:
- Scalars have magnitude only; Vectors have magnitude and direction.
- Speed is distance/time; Acceleration is change in velocity/time.
- 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.
- Always remember the standard value for gravity: \(g = 10 \text{ m/s}^2\).
- Cross-reference: To see how these motions are caused, look at the next chapter on Newton's Laws.

Quick check

Can you answer these now?

Open each question to check the key ideas from this chapter.

What is a scalar quantity?

A scalar quantity is a physical measurement that has magnitude (size) only, without a specific direction.

What is a vector quantity?

A vector quantity is a physical measurement that has both magnitude (size) and a specific direction.

What is the difference between distance and displacement?

Distance is a scalar representing the total path traveled, while displacement is a vector representing the straight-line distance and direction from the start to the end point.

What is the formula for calculating average speed?

\(\text{distance travelled} = \text{average speed} \times \text{time}\)

What are the typical walking, running, and cycling speeds for a human?

Walking: \(\approx 1.5 \text{ m/s}\); Running: \(\approx 3 \text{ m/s}\); Cycling: \(\approx 6 \text{ m/s}\).

How is acceleration defined and calculated?

Acceleration is the rate of change of velocity, calculated as \(a = \frac{v - u}{t}\), where \(v\) is final velocity, \(u\) is initial velocity, and \(t\) is time.

What is the acceleration due to gravity on Earth (\(g\)) for the Edexcel exam?

\(g = 10 \text{ m/s}^2\)

What is the equation linking final velocity, initial velocity, acceleration, and distance?

\(v^2 - u^2 = 2 \times a \times x\)

What does the gradient of a distance-time graph represent?

The gradient (slope) of a distance-time graph represents the speed of the object.

What do the gradient and the area under a velocity-time graph represent?

The gradient represents acceleration, and the area under the graph represents the distance travelled.

Why are light gates preferred over stopwatches in physics experiments?

Light gates are more accurate because they eliminate errors caused by human reaction time.

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