Introduction

Motion Is All Around Us

Motion is one of the most universal facts of nature. We walk, run, cycle; even while we sleep, air moves in and out of our lungs and blood circulates through our arteries and veins. Leaves fall from trees, water flows down a dam, cars and aircraft carry people from place to place. On a much larger scale, the Earth spins on its axis once a day and orbits the Sun once a year, and the Sun itself drifts through the Milky Way, which is in turn moving within its cluster of galaxies. Motion is not a special case to be studied only in the laboratory — it is the default state of almost everything in the universe.

What This Chapter Covers

To describe motion quantitatively, this chapter builds up the following ideas, roughly in this order:

• Velocity — how fast position changes, and in which direction.
• Acceleration — how fast velocity itself changes.
• Rectilinear motion — we restrict attention to motion along a single straight line (also called one-dimensional or rectilinear motion), which keeps the mathematics simple while still capturing the essential physics.
• Kinematic equations for uniform acceleration — once acceleration is constant, a compact set of equations connects position, velocity, acceleration and time.
• Relative velocity — motion is never absolute; how an object's motion appears depends on the observer, so the chapter closes by making this "relative" nature precise.

The Point-Object Approximation

Throughout this chapter (and much of the mechanics that follows), a moving object is treated as a point object — its size and internal structure are ignored, and only the position of a single representative point is tracked. This is a valid simplification whenever the size of the object is much smaller than the distance it travels in the time being considered. A car travelling several kilometres, or a train travelling between stations, can safely be treated as a point even though it is metres long — the error introduced is negligible. The approximation would break down, however, for very short motions comparable to the object's own size (for example, describing the motion of a train as it pulls out of a platform only a few metres long).

Kinematics: Describing Motion Without Asking Why

This chapter belongs to a branch of mechanics called kinematics — the study of how to describe motion (in terms of position, velocity and acceleration) without asking why the object moves the way it does. The question of what actually causes a change in motion — forces — is deliberately set aside here and taken up later, beginning with the laws of motion. So while this chapter (and the one that follows) develops the language and mathematics for describing motion, the physical causes behind that motion are a separate subject built on top of it.