1.Kinematics

1. Kinematics

(Last Updated 08/18/2025, 14:35 MST)

1.1 Scalars and Vectors in One Dimension

A scalar is a physical quantity, including units of measurement, that can be described by a single real number.

A vector is a geometric object that has magnitude (or length) and direction. A vector quantity is usually a physical quantity, including units of measurement, formulated as a directed line segment. A vector is frequently depicted graphically as an arrow connecting an initial point A with a terminal point B. A vector is what is needed to "carry" the point A to the point B; the Latin word vector means 'carrier'. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from A to B.

A vector in one dimension will not have a direction other than from A to B, or B to A, where both A and B are on the same coordinate axis.

Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogs for vector operations which obey the familiar algebraic laws of commutativity, associativity, and distributivity. Vectors play an important role in physics: the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors. Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (except, for example, position or displacement), their magnitude and direction can still be represented by the length and direction of an arrow. The mathematical representation of a physical vector depends on the coordinate system used to describe it.

1.2 Displacement, Velocity, and Acceleration

Displacement is the change in position of an object. It's a vector quantity, meaning it has both magnitude (how far the object moved) and direction. For example, if an object moves 10 meters to the east, its displacement is 10 meters east.

Velocity is the rate of change of displacement. It's also a vector quantity. It tells you how fast an object is moving and in what direction. For instance, if an object is moving at 5 meters per second to the north, its velocity is 5 m/s north.

Acceleration is the rate of change of velocity. It's also a vector quantity. It describes how quickly the velocity of an object is changing. If a car speeds up, it's accelerating. If it slows down, it's also accelerating (but in the opposite direction).

In simpler terms, displacement tells you where an object is relative to its starting point, velocity tells you how fast it's moving and in what direction, and acceleration tells you how quickly its velocity is changing. These three concepts are fundamental to understanding how objects move in physics.

1.3 Representing Motion

Page 38 - Reading: Motion Maps

Page 39 - Reading: Motion Maps

1.4 Reference Frames and Relative Motion

1.5 Vectors and Motion in Two Dimensions