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!