What does v=dx/dt means?
It represents the instantaneous variation of POSITION with TIME. also known, as velocity.
The explanation can be a little bit boring but…
Cosider a car that moves from position ##x_1## at instant ##t_1## to position ##x_2## at instant ##t_2##.
You can represent the variation of position using a number (a kind of position parameter) called average velocity as:
##v_(av)=(x_2-x_1)/(t_2-t_1)=(Deltax)/(Deltat)##
The problem is: “what happened in the middle? Did the car stop…go faster…slower…?”
To “look” inside your interval you can reduce the time interval and try to focus on a specific instant.
This means reducing ##Deltat## to zero or at least tend to zero!
So, basically, you’ll be able to evaluate the velocity at a point (not interval) and have an instantaneous velocity!
It is easy to say but mathematically…you need:
##v_(“inst”)=lim_(Deltat->0)(Deltax)/(Deltat)=(dx)/(dt)## which is the “symbol” for an operation done on a function called Derivative.
For example:
consider a car that has a position modelled by the function:
##x(t)=-4t^2+3t-2## (I invented it)
So
instantaneous velocity will be given as:
##(dx)/(dt)=-8t+3##
So at each instant you will get the velocity at exactly that instant: for example at ##t=0## ##v_(“inst”)=-8*0+3=3m/s##
Hope it is not too confusing!