- #1

fog37

- 1,568

- 108

Limiting our discussion to 1D motion, it is clear that the concept of instantaneous velocity is defined as the covered displacement dx divided by the

**time**interval elapsed dt:

$$ v = \frac {dx}{dt}$$

However, mathematically, the velocity ##v## can be made to depend on any parameter ##t,x,a##. For example the velocity ##v## can be expressed a function of time ##v(t)## but also as a function position ##v(x)##. If we know the position function ##x(t)##, we can substitute that into ##v(x) = v( x(t))## to obtain ##v(t)##. If ##x(t) =3t+2## and ##v(x) = x ^2##, then ##v(t)= (3t+2)^2##.

- The three functions ##v(t)## and ##x(t)## ##v(t)## cannot be independent of each other because the object's motion is one and only one and the three functions cannot provide contradictory information about the motion, correct?
- Would it be possible to have a situation where the velocity is a function of both position and time ##v(x,t)##? Would you have a simple example of functions that would result in that?