Displacement is an example of a vector quantity. Distance is an example of a scalar quantity. A vector is any quantity with both magnitude and direction.
Coordinate Systems for One-Dimensional Motion. Solution Speed is a scalar quantity. It does not change at all with direction changes; therefore, it has magnitude only. If it were a vector quantity, it would change as direction changes even if its magnitude remained constant. Conceptual Questions 1. What is the speed of the bird?
Glossary scalar: a quantity that is described by magnitude, but not direction vector: a quantity that is described by both magnitude and direction. There are several vector quantities including:.
The term acceleration can refer to a scalar acceleration or an acceleration vector. Treat acceleration as a vector when there is another vector quantity, such as velocity or force, involved in a question. The relationship between distance, speed and acceleration can be applied to displacement, velocity and acceleration. Ultimately I suppose one comes to some irreducible definitions, where one throws up one's hands and asks whether we're just going to talk about stuff or do something interesting with what we all just know, until someone points out persuasively that we don't and that it's useful to just know something different.
I reckon it describes a non-commutative relationship between two objects or events which is completely determined by their position in some measurable space, independent of their distance by some well defined measure of distance and some set of operations on both of them probably just translation really.
As an aside, I guess you could use a method more suited to analytical philosophy. If I wanted to examine what a direction as used by physicists was, I would do something like: 1 Acknowledge that most physicists would agree on what a direction is. Take the tangent vector at the start of the shortest path between a pair of distinct points, and mod out by distance. What you have left is "direction".
In a Euclidean space with a standard metric, you can do this by just dividing any non-zero vector by its length. The resulting normalized vector is a "direction". For curved spaces, it is a bit more complicated, but still the same basic idea. Simply: Points are well defined in a space e. Now consider two points. One can assign two information to these two points 1 distance and 2 direction.
I skip the concept of the distance. The choice or information of which point be first and the other be second point defines the direction. At a basic level, a vector is construced from the difference between two coordinates a-b.
The number that represents the distance between them is the magnitude of displacement vector ab. There is nothing else, certainly no direction intrinsic to it. Introducing a third coordinate means you can define a second displacement vector ac. That's one way of doing it, but essentially you're just assigning a number to a pair of vectors.
Direction is measured by angle and therefore is a function that assigns a number to two vectors. It isn't intrinsic to a vector. The definition of direction is by three numbers a,b,c which represent the components of a vector along an arbitrary x-axis, y-axis, and z-axis.
But if you ignore the motivation, a vector is a triplet of numbers. This reduces the description of direction to the description of real numbers, and has been the standard definition since the time of Descartes. The reason this definition took so long to formulate is because there is an arbitrariness in the choice of coordinates.
Given a collection of directions triplets of numbers which describe a physical situation, one can always transform all the directions by a rotation matrix which is defined noncircularly as a matrix all of whose columns are perpendicular to each other and have unit length , and the situation is not altered. Because of the rotation business, mathematicians are often uncomforable with the definition of direction by triplets of numbers, but this is really the best way, since all other methods are more complicated and needlessly so.
Start Your Free Trial Learn more. Matt Jones M. Explanation Transcript A vector contains two types of information: a magnitude and a direction. Physics Linear and Projectile Motion. Science Biology Chemistry Physics. English Grammar Writing Literature.
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