# Instantaneous velocity - displacement and distance

• I
Instantaneous velocity is defined as the first derivative of displacement with respect to time:

##\vec{v} = \dfrac{d \vec{r}}{dt}##
However, instantaneous velocity is also defined as the first derivative of function of distance with respect to time:

##v = \dfrac{ds}{dt}##
Why do these two different quantities result in the same thing? We can certainly find the distance traveled between two points if we know the displacement function, why?​

Instantaneous velocity is defined as the first derivative of displacement with respect to time:

##\vec{v} = \dfrac{d \vec{r}}{dt}##
However, instantaneous velocity is also defined as the first derivative of function of distance with respect to time:

##v = \dfrac{ds}{dt}##
Says who and where? Except as a special case in a one-dimensional setting?

Why do these two different quantities result in the same thing?​
They do not. Not generally.

PeroK
Orodruin said:
Says who and where? Except as a special case in a one-dimensional setting?

They do not. Not generally.
How would you explain it in “special” one dimensional case?

The (signed) distance from the origin is the position in one dimension.

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