Instantaneous measurement of nonlocal variables

The average velocity during a time interval cannot tell us how fast or in what direction a particle is moving at any given time during the interval. To calculate this, it is important to know the instantaneous velocity, which is the velocity at a specific instant of time or at a specific point along the path. Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity vx of an object is the limit of the average...

Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity of an object is the limit of the average velocity as the elapsed time approaches zero, or the derivative of displacement with respect to time. Like average velocity, the instantaneous velocity is a vector with the dimensions of length per unit time. Instantaneous velocity can have both positive and negative values. The instantaneous velocity can be...

Acceleration is in the direction of the change in velocity, but it is not always in the direction of motion. When an object slows down, its acceleration is opposite to the direction of its motion. Although commonly referred to as deceleration, this causes confusion in our analysis as deceleration is not a vector, and does not point to a specific direction with respect to a coordinate system. Therefore, the term deceleration is not used. For example, when a subway train slows down, it...

To calculate other physical quantities in kinematics, the time variable must be introduced. The time variable not only allows us to state where an object is (its position) during its motion, but also how fast it’s moving. The speed at which an object is moving is given by the rate at which the position changes with time. For each position, a particular time is assigned. If the details of the motion at each instant are not important, the rate is usually expressed as the average velocity v. This...

General plane motion, often observed in a rolling wheel, refers to a type of movement where the wheel is simultaneously rotating and translating. This complex motion can be understood by breaking it down into individual components.
To analyze this, consider two points on the wheel: point A and point B. The absolute velocity of point B can be expressed as the vector sum of the absolute velocity of point A and the relative velocity of point B with respect to point A. To simplify this analysis,...

The highest and lowest values of a function, relative to a reference axis, are known as extreme values. These include absolute maximum and absolute minimum values, which represent the highest and lowest points the function reaches across its entire domain. Within a restricted portion of the function, the highest and lowest values are referred to as local maximum and local minimum values, respectively.Periodic functions, such as sine and cosine, show extreme values at infinitely many points due...