Velocity

The average speed of an object is defined as the distance traveled divided by the time elapsed. The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.

Velocity is a vector quantity, and average velocity can be defined as the displacement divided by the time. The units for velocity can be implied from the definition to be meters/second or in general any distance unit over any time unit. For the special case of straight-line motion in the x direction, the average velocity takes the form:

\[v_{avg}=\overline{v}=\dfrac{x_2-x_1}{t_2-t_1}\]

You can approach an expression for the instantaneous velocity at any point on the path by taking the limit as the time interval gets smaller and smaller. Such a limiting process is called a derivative and the instantaneous velocity can be defined as:

\[v_{inst}=\lim_{\Delta t\rightarrow 0}\dfrac{\Delta x}{\Delta t}=\dfrac{dx}{dt}\]

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