In physics, we define quantity as anything that can be assigned a number or a set of numbers to it. Physics is fundamentally a quantitative science, and therefore everything we cannot measure is meaningless. In terms of the type of numbers that can be assigned to a specific quantity, the quantities are divided into two distinct types. continuous quantities that contain all possible values, and discrete quantities that cover only discrete values that are usually represented as correct coefficients of a certain initial value.
The process of estimating the value of a property (such as length, weight, and time), relative to a specific module or certain unit of each property by a scientific tool with definite precision, is called measurement. Measurement in physics is, in fact, a tool for determining the empirical validity of laws or theories, which, as they have been said, are expressed as mathematical propositions.
The measurement unit is a definite magnitude of a quantity which has a dimension, and measuring the value of a physical property is done by comparing to it. Different units are defined for each fundamental quantity, and the one corresponding to a quantity can be converted to only the other ones of the same quantity.
Each measure has a number and a dimension: dimension is an indicator that gives a mathematical number real and physical meanings. Otherwise, the numbers will be meaningless to us.
Physical quantities are in two types:
Scalar Quantities: Quantities that only have magnitude. Like: mass, time, temperature, etc.
Vector Quantities: Quantities that in addition to magnitude, have direction. Such as: speed, displacement, force, etc.
These two types of quantities also uniquely behave to mathematical operations, and each one desires its own particular operations. For example, calculations for scalar quantities can be made by simple mathematical summation and multiplication. But in the case of vector quantities, doing so is not possible and it is necessary to use special operations for vector quantities.
As it seems at first glance, the broadness of the concepts of physics makes it impossible to arrange definitions and units. But all the concepts of physics are not independent, but are usually the result of relations between the units of quantities that we call the major quantities (length, mass, time, etc.).
Some of the major quantities, such as mass, are fundamental concepts in physics and have an intuitive basis. While from some of the sub-quantities such as speed, various concepts can be derived. for example:
The average speed is defined as the ratio of the distance traveled to the elapsed time.
The speed is defined as the magnitude of velocity of the object.
The instantaneous velocity is an intuitive sense of speed that can be understood by observing the velocity in a speedometer.