Why doesn't an electric charge use up all its potential energy travelling from positive to negative terminal?
Speed of electrons

You are still struggling with the concept of charge and current raised in your [previous question]
(If an electron has 0 electric potential after passing through a resistor, how does it flow to the other terminal). Let's deal with your question first.


  E.g. A ball which is lifted above the ground has potential energy and all the energy is converted to kinetic energy to move to the ground when released.


This isn't a good analogy for a current. At the instant the ball is released it still has all the potential energy and zero kinetic energy. As the ball accelerates due to gravity the potential energy decreases (due to loss of height) and the kinetic energy increases (due to increased velocity). An electrical analogy of this would be an electron beam in a vacuum tube where the effect on a single electron and its acceleration from cathode to anode can be considered.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Electron current in a thermionic valve / tube.

Have a look at the Wikipedia article on drift velocity. It shows the calculations for a current I = 3 amperes, and a wire of 1 mm diameter and comes up with the result that in this wire the electrons are flowing at the rate of −0.0000028 m/s. At this rate it would take 99 hours for an electron to travel 1 m along that wire! If we double the current the time taken is halved.

As the electrons move through the resistive material they interact with the atoms in that material and that's what limits the current.

Speed of electricity

With reference to Wikipedia's Speed of electricity: 


  The speed at which energy or signals travel down a cable is actually the speed of the electromagnetic wave, not the movement of electrons. Electromagnetic wave propagation is fast and depends on the dielectric constant of the material. In a vacuum the wave travels at the speed of light and almost that fast in air.


The speed of the electric current will be somewhere between 50% and 99% of c, the speed of light (\$3 \cdot 10^8~m/s\$). See Wikipedia's Velocity factor for more information.

The end result

The electrical current is a very slowly moving jostling of electrons through the conductor. The propagation of the wave is very fast. Think of a line of marbles in a pipe. If we push a marble in one end a marble will pop out the other end immediately despite the fact that each marble has only moved one marble diameter.

Stop thinking of charge. Start thinking of current.