Introduction to Motion Along a Straight Line

Welcome to one of the most fundamental chapters in your AQA AS Physics course! This topic is part of the Force, Energy and Momentum section. Everything in physics starts with understanding how things move. Whether it's a car braking, a sprinter starting a race, or a ball falling to the ground, we use the same set of rules to describe their journey.

In this chapter, we focus strictly on linear motion—movement in a straight line. We will learn how to describe this motion using numbers, graphs, and some very famous equations. Don't worry if the math looks intimidating at first; once you see the patterns, it becomes much easier!

1. Describing Motion: The Big Four

To talk about motion like a physicist, we need to distinguish between four key terms. Some are scalars (just size) and some are vectors (size and direction).

Displacement (\(s\)) vs. Distance

Distance is a scalar. It is the total ground covered (e.g., "I walked \(100\) meters").
Displacement is a vector. It is the straight-line distance from your starting point to your finishing point, including the direction (e.g., "\(100\) meters North").

Velocity (\(v\)) vs. Speed

Speed is how fast you are going (scalar).
Velocity is speed in a given direction (vector).
The formula for average velocity is:
\(v = \frac{\Delta s}{\Delta t}\)
(Where \(\Delta s\) is change in displacement and \(\Delta t\) is change in time)

Acceleration (\(a\))

Acceleration is the rate of change of velocity. If you speed up, slow down, or change direction, you are accelerating.
\(a = \frac{\Delta v}{\Delta t} = \frac{v - u}{t}\)
The unit for acceleration is \(\text{ms}^{-2}\) (meters per second squared).

Quick Review:
  • Displacement: Vector version of distance.
  • Velocity: Vector version of speed.
  • Acceleration: How quickly velocity is changing.

2. Graphical Representation of Motion

Graphs are a visual way to tell the "story" of a journey. For your exam, you must know what the gradient (slope) and area represent.

Displacement-Time (\(s-t\)) Graphs

This graph shows where an object is over time.

  • Gradient: Represents the velocity.
  • A straight diagonal line means constant velocity.
  • A horizontal line means the object is stationary (velocity = \(0\)).
  • A curve means the object is accelerating or decelerating.

Velocity-Time (\(v-t\)) Graphs

This is the most important graph in this chapter!

  • Gradient: Represents the acceleration.
  • Area under the graph: Represents the displacement (distance traveled).
  • A horizontal line means constant velocity (zero acceleration).
  • A straight diagonal line means uniform (constant) acceleration.

Top Tip: If a \(v-t\) graph goes below the x-axis, the object has changed direction and is moving backward!

3. The SUVAT Equations (Uniform Acceleration)

When an object is moving with constant acceleration, we use five equations known as the SUVAT equations. Each letter stands for a variable:

  • \(s\) = displacement (\(\text{m}\))
  • \(u\) = initial velocity (\(\text{ms}^{-1}\))
  • \(v\) = final velocity (\(\text{ms}^{-1}\))
  • \(a\) = acceleration (\(\text{ms}^{-2}\))
  • \(t\) = time (\(\text{s}\))

The Equations:

  1. \(v = u + at\)
  2. \(s = \frac{(u + v)}{2}t\)
  3. \(s = ut + \frac{1}{2}at^2\)
  4. \(v^2 = u^2 + 2as\)
How to solve SUVAT problems:
  1. List the variables you know (you usually need three).
  2. Identify the variable you want to find.
  3. Choose the equation that uses those four variables.
  4. Rearrange and solve!

Common Mistake: Using these equations when acceleration is NOT constant. If acceleration changes, you must use a graph instead!

4. Acceleration Due to Gravity (\(g\))

When an object falls freely under gravity (ignoring air resistance), it accelerates at a constant rate. This is known as acceleration due to gravity, represented by the symbol \(g\).

On Earth, \(g \approx 9.81 \, \text{ms}^{-2}\).

Key Rules for Vertical Motion:
  • When an object is dropped: \(u = 0\) and \(a = 9.81 \, \text{ms}^{-2}\).
  • When an object is thrown upwards: At its highest point, \(v = 0\).
  • Gravity always acts downwards, so be careful with your signs (\(+\) and \(-\))! If you choose "up" as positive, then \(g\) must be negative (\(-9.81\)).

5. Required Practical 3: Determination of \(g\)

You need to know how to determine the value of \(g\) experimentally. A common method is the Free-Fall Method.

The Setup:

  • An electromagnet holds a small steel ball over a trapdoor.
  • When the current is switched off, the ball falls and a timer starts.
  • When the ball hits the trapdoor, the timer stops.
  • Measure the height (\(h\)) the ball falls.

The Calculation:

Using the SUVAT equation \(s = ut + \frac{1}{2}at^2\):
Since the ball starts from rest (\(u = 0\)) and displacement is height (\(h\)), the equation becomes:
\(h = \frac{1}{2}gt^2\)

The Graph:

If you repeat the experiment for different heights and plot a graph of \(h\) on the y-axis against \(t^2\) on the x-axis:
The gradient of the line will be \(\frac{g}{2}\).
Therefore: \(g = 2 \times \text{gradient}\).

Did you know? Even though gravity is roughly \(9.81 \, \text{ms}^{-2}\), it varies slightly depending on where you are on Earth because the planet isn't a perfect sphere!

Summary Checklist

Before moving on to Projectile Motion (Section 3.4.1.4), make sure you can:

  • Define displacement, velocity, and acceleration.
  • Calculate velocity from the gradient of an \(s-t\) graph.
  • Calculate acceleration from the gradient of a \(v-t\) graph.
  • Calculate displacement from the area under a \(v-t\) graph.
  • Memorize and apply the SUVAT equations for constant acceleration.
  • Describe the free-fall experiment to determine \(g\).