How do I explain that there is no instantaneous velocity at a sharp turn?

Question

Suppose that a one-dimensional motion is describe by the function $s(t)=\begin{cases} t , & 0 \leq t \leq 5;\\ 10 - t, & 5 < t \leq 6\end{cases}$,

where $t$ is a time and $s(t)$ is the distance travelled at $t$. The motion described by this function has a sharp turn at $t=5$, and $s$ is not differentiable at that point. Does this mean that there is no instantaneous velocity at $t=5$? If so, how would you interpret it physically?

Answer 1

That is correct, the instantaneous velocity is undefined at $t=5$ in this case. This describes an infinite acceleration at $t=5$ so the physical interpretation is that this is a physically impossible scenario (requiring an infinite force) so the fact that the velocity is undefined is just a symptom of using a physically unrealistic scenario.