Are we teleporting?

[robvalue]

Might want to try "discrete"

We can use calculus to determine the speed of something moving continuously. This speed is given as the limit of distance/time as you approach ever closer to that point. This applies to our models of motion, and doesn't necessarily mean continuous motion is actually happening. But if it was, the analysis would be sound.

For example:

Say f(t) = t^2 is the distance travelled after time t.

If we take a particular point in time x, and a time very shortly after it x+h :

Average speed in this interval = difference in distance / difference in time =[ (x+h)^2 - x^2 ] / h

= [x^2 +2hx + h^2 - x^2] / h

=[2hx + h^2] / h

=2x + h

Now we let h tend towards zero, to find the speed exactly when t = x

Speed = 2x

So the speed at any point t is 2t. No infinite speed involved Speed is the rate of change of distance travelled; at each point, the rate of change is equal to twice the time elapsed.

We can achieve this result much more quickly by "differentiation". The derivative of t^n is n*t^(n-1) so in this case, n=2 and the derivative is 2*t^(1) = 2t