Question #02291

May 23, 2016

No, most of the time if something is undefined in physics it means you're missing something and the model doesn't apply any more (leaving out friction is a great way of getting infinities that doesn't exist in the real word).

Explanation:

${v}_{x} \ne \frac{{d}_{x}}{{t}_{x}}$

so, ${v}_{0} \ne \frac{{d}_{0}}{{t}_{0}}$

nor is it $\frac{\Delta d}{\Delta t}$.

Recall, ${v}_{a v e r a g e} = \frac{\Delta d}{\Delta t}$

The true definition of velocity is this :

$\vec{v} \left(x\right) = {\lim}_{\Delta t \rightarrow 0} \frac{\vec{d} \left(x + \Delta t\right) - \vec{d} \left(x\right)}{\Delta t}$ .

so at $x = 0$ we have

$\vec{v} \left(0\right) = {\lim}_{\Delta t \rightarrow 0} \frac{\vec{d} \left(0 + \Delta t\right) - \vec{d} \left(0\right)}{\Delta t}$

And that limit makes all the difference (you'll learn about about this in calculus).

Recall that special relativity explains that that NOTHING with mass can reach the speed of light, and things without mass like photons ONLY travel at the speed of light.

There is a speed limit on the universe of $3.00 \times {10}^{8}$ $\frac{m}{s}$ .

So nothing has infinite speed, infinite speeds only occur due to limits in a physical model.