Throw Ball: Max Height & Velocity = 0

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When a ball is thrown upward, its velocity reaches zero at the peak of its trajectory, but this zero velocity is instantaneous, lasting no measurable time. The discussion highlights that while velocity changes continuously, it only passes through zero without remaining there. The concept of measuring time as infinite is debated, with some arguing that it contradicts the idea of instantaneous events. Non-standard analysis is mentioned as a framework that can accommodate instantaneous values. Ultimately, the conversation centers on the nature of velocity and time in kinematic equations.
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in a kinematic equation when you throw a ball up and it reaches its highest point its velocity becomes zero how long is it zero
 
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In the idealized description of the trajectory, its speed is zero instantaneously, i.e. the duration of zero speed is itself zero! Ultimately, of course, your measurements have limited resolution and air turbulence will contribute to uncertainty.
 
or more simply, the velocity is always changing, it is never constant, so the velocity never stays at any value. It passes through the value zero at a certain time,but it does not stay that value.
 
in my thinking that there are infinite numbers so you could measure time presicely infinite so something being instantaneous would not be possible
 
jlorino said:
in my thinking that there are infinite numbers so you could measure time presicely infinite so something being instantaneous would not be possible

"measure time precisely infinite" makes no sense. In any case, I would think "there are infinite numbers" would mean that you CAN have something "instantaneous"- that's basically what non-standard analysis is about.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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