# 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

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

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