Question

What is the derivative definition of instantaneous velocity?

Answer 1

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

instantaneous velocity=
`v`= `lim_(Delta t -> 0)` `(Delta x)/(Delta t)`= `dx/dt`

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=6t^2+t+12`

Since `v`=`dx/dt`, `v= d/dt 6t^2+t+12= 12t+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 (m)/(sec)`