Instantaneous Velocity and Acceleration
Instantaneous Velocity and Acceleration
\[\vec{v} = \lim_{\Delta t \to 0}\dfrac{\Delta s}{\Delta t}\]
\[\vec{a} = \lim_{\Delta t \to 0}\dfrac{\Delta v}{\Delta t}\]

To define and calculate the instantaneous velocity and speed.

To differentiate between average and instantaneous velocity.

To calculate the average acceleration and determine its direction.

To calculate the instantaneous acceleration from position function or velocity function and determine its direction.
The instantaneous velocity is obtained as follows: \[\vec{v} = \lim_{\Delta t \to 0}\dfrac{\Delta s}{\Delta t}\] Or, if s = f(t) then v = \(\dfrac{d}{dt}f(t)\) = f’(t)
The instantaneous acceleration is obtained as follows: \[\vec{a} = \lim_{\Delta t \to 0}\dfrac{\Delta v}{\Delta t}\] Or, if v = g(t) then a = \(\dfrac{d}{dt}g(t)\) = \(\dfrac{d^2}{dt^2}f(t)\)