Object projected vertically upwards and Planck time

[skepticwulf]

When we throw an object vertically , its speed decreases due to gravity and comes to a halt at the very top, V=0 and starts falling down.
What can we say about that "halt" moment? Is it defined in terms of seconds? Does it last as long as Planck time? being the smallest measurement of time that has any meaning?

 

[Nugatory]

You are misunderstanding what the Planck time is. That's a very common misunderstanding, so common that we even have an Insights article on the subject: https://www.physicsforums.com/insights/hand-wavy-discussion-planck-length/

You could say that the object is stationary for zero seconds (and zero years, and zero milliseconds) if you wish - zero is zero no matter what units you use.

 

[skepticwulf]

Does that mean Velocity was 0 for 0 seconds? In other words, Velocity was never 0?
Does that mean velocity came to 0 by every instant it approached to the top but NEVER became 0 and turned down immediately BEFORE being zero?

 

[Nugatory]

It means that there is a time $t_0$ such that $v(t_0)=0$, but that for any non-zero value of $\epsilon$, no matter how small, $v(t_0\pm\epsilon)$ is not zero.

Note that there is nothing special about the zero speed here. If the object was initially thrown upwards at five meters/sec, there is a moment when the object is moving at exactly three meters/sec. What can we say about that moment? How long does it last? We can ask these questions about any speed.

 

[skepticwulf]

I think it's "classical" thinking that makes me think erroneously. One tends to think the ball comes into a complete halt at V=0, hangs there for intimately small -but for true- duration and THEN starts falling down.
When you consider "there is nothing special about the zero speed", then it's clear.
You can look at its picture when V=3m/s or 0m/s. The "moment" is virtually the same.
Thank you.