Our teacher told us that, in real life, a displacement vs. time graph will always be smooth. This made sense to me because force is always finite, which implies finite acceleration as well. I was wondering if this smoothness extends to all higher derivatives of displacement, like velocity, acceleration, jerk, and so on.
Is it true that these graphs will always be smooth in real-life scenarios?
How can this be proven, mathematically or conceptually?
Are there cases in nature where this assumption might break down?
I feel a bit stuck on how to approach this problem or where to begin analyzing it. Could someone guide me on how to frame this or provide a starting point for understanding?
