What is the derivative definition of instantaneous velocity?

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Emily Green · Accepted Answer

Instantaneous velocity is the change in position over the change in time. Therefore, the derivative definition of instantaneous velocity is:
instantaneous velocity=

v = lim_{△ t \to 0} \frac{△ x}{△ t} = \frac{d x}{d t}

So basically, instantaneous velocity is the derivative of the position function/equation of motion. For example, let's say you had a position function:

x = 6 t^{2} + t + 12

Since

v = \frac{d x}{d t}, v = \frac{d}{d t} 6 t^{2} + t + 12 = 12 t + 1

That is the function of the instantaneous velocity in this case. Note that it is a function because instantaneous velocity is variable- It is dependent on time, or the "instant." For every t, there is a different velocity at that given instant t.
Let's say we wanted to know the velocity at t=10 and the position is measured in meters (m) while the time in measured in seconds (sec).

v = 12 (10) + 1 = 121 \frac{m}{\sec}

What is the derivative definition of instantaneous velocity?

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