The Velocity Function in One Dimension
The Velocity Function
The velocity function is the time-deravitive of the position function. Repeat this seven times. Memorize this. There is an infinite number of mathematical representations of this relationship depending on the specific circumstances. However, the fundamental relationship between the velocity and the position is the same: The function that describes the velocity of an object is the derivative (with respect to time) of the function that describes the position of the object.
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Graphical Representation of Velocity and Position
It is important to know how to represent physics ideas with different representations. This greatly improves your ability to solve problems. The graphical representation of kinematics is so important, that in nearly all courses on this subject, you will be tested over your knowledge of and proficiency with them.
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Average Speed and Average Velocity
Now, we want to look at the differences between average speed and average velocity. Spoiler alert! They are not the same thing.