The division of meters by seconds in the expression "meters per second" is a way to represent the rate of change of position over time. It is a mathematical convention used in physics and other scientific disciplines to describe the concept of velocity.
Velocity is defined as the rate at which an object changes its position in a particular direction. It is determined by dividing the change in position (in meters) by the time taken for that change (in seconds). This division is used to express the ratio of the distance traveled to the time taken, resulting in a quantity that represents how many meters an object moves in one second.
Mathematically, dividing meters by seconds does not involve the idea of the number of times the denominator goes into another, as you mentioned. Instead, it represents the ratio of two quantities with different units: meters and seconds. This ratio allows us to quantify the speed or rate at which an object is moving, indicating how far it travels in a given time interval.
By expressing velocity as meters per second, we can compare the speeds of different objects or analyze how the velocity of an object changes over time. This standardization of units enables scientists, engineers, and other professionals to communicate and work with consistent measurements across various fields and applications.