You throw throw the ball upward giving it an initiall upward velocity and as it rises the downward tug of gravity on the ball will slow the ball's upward motion until tthe ball reaches its greatest altitude with zero upward velocity and begins accelatered fall downward under gravity to pass through the point where you released it with a downward velocity equal in magnitude to the upward velocity it had when it left your hand. We ignore air resistence.

Dear R. C. Storti,

you can draw a diagram for the velocity over time. It will be a straight line. There is only one instant in time where the velocity is zero (one point along the line). Thus, the time that the ball has velocity zero is infinitesimally short.

Kind regards,

Sascha Grusche

Thanks I appreciate your reply, but I am hoping to find an experimental measurement of what that infinitesimally short period actually is; rather than a theoretical assumption. I'm asking the question. 'is it EXACTLY 0(s)' or xE-Y(s) ?

To reverse the movement the ball must necessarily stop, then its speed is exactly zero.

I understand that in your question you want to know what time remains in that state?

If you want to experimentally determine how long the ball has zero speed, obviously you would have to measure its speed. How? Possibly through some use of the Doppler effect (as police radar "guns" do) or maybe by measuring changes in the ball's position. But any such attempts will have some errors of measurement, and due to those experimental errors, there will be some interval of time in which the speed is indistinguishable from zero. You can try to make the measurements more and more accurately, but you can never do it with perfect precision, and thus there always will remain some short interval of time when its measured speed is indistinguishable from zero. (And I'm not even going to try to bring the uncertainty principle into this discussion.) Of course, theoretically, the ball's speed is zero only for an infinitesimally short instant of time, but measuring it always will involve some experimental imprecision.

Thanks everyone, Diego de Jesús Alamino Ortega has framed my question precisely correct ..... How long will the ball have 0(m/s^2) .... I'm hoping to find an experimental measurement of this value (if it has ever been done before). I know it will be a very very short period, but it can't be exactly instantaneous, it must have some non-zero time value, surely.

Thanks Richard Erickson, I agree. The thing is, I can't execute that kind of measurement myself, so I was hoping that someone might know the answer (the actual experiment) or point me in the right direction to get it.

The point is that any measured time of zero speed is just an artifact of the imprecision of the measurements. I have no idea how accurately in practice the measurements could be made, but why would anyone bother to go to the time and effort? Any measured non-zero time would be physically meaningless, since with improved accuracy the measured time would get smaller and smaller, approaching zero as measuremental imprecision is reduced.

Here is the link to a video that answers the question

https://www.khanacademy.org/science/physics/one-dimensional-motion/kinematic-formulas/v/projectile-height-given-time

Thanks for that Dwight Hoxie , it was a really cool video & the presenter has a great teaching style. But unfortunately, it doesn't exactly answer what I'm trying to find out. What I really want to know (by physical measurement) is how long it sits with zero velocity at the peak of its displacement. In theory, it's zero time at zero velocity at its peak displacement (then it reverses direction) ..... What I really want to know is if theory actually matches experiment to high precision ..... I know the experiment I'm talking about seems trivial, but has it actually been done ? .... I'm after this information to help me solve another problem involving impulse & momentum transfer; that's why I'm curious about it

Riccardo, it sits with zero velocity for an infinitesimal amount of time. Which experimentally means, if it appears to sit at zero velocity for any amount of time at all, it is only because the measuring equipment has to "sample and hold," in order to give results. It is an artifact of the measuring equipment. (By the way, even our eyes work that way. What we see is not truly continuous.)

If a force is applied to a mass, and the force is never removed, that mass will continue to accelerate always. In the experiment you describe, gravitational force is steady. Therefore, the mass must always accelerate. No interruption. Which means, velocity must change constantly, no exception. (I assume classical physics is sufficient, for this experiment.)

Thanks Albert, I appreciate your thoughts & I see your argument about the force being applied constantly (a good argument by the way). Based upon your point, I think I have chosen a poor analogy for the problem I am trying to solve. I think you've answered the question elegantly; the value must be instantaneous via the logic you have presented.

Nevertheless, I am curious to know if someone has actually done the experiment.

Dear R. C. Storti,

I have done an experiment with a ball in air. I have made a video and analyzed individual frames. You can make a height-versus-time diagram. From the slope of the tangent, you can determine the velocity. As far as I know, it is impossible to measure velocity as such, it will always be based on measurements of distances over time.

Kind regards,

Sascha Grusche

Thanks for that Sascha Grusche , you have done much more to help that I should expect or deserve; really appreciate all your help ..... In fact, thanks to everybody here.

Riccardo, I've come up with a way to respond to the question about "has anyone measured this, and come up with an amount of time in which the velocity is zero."

And my answer, before the explanation which follows, would be, it does not matter whether anyone has come up with a time period. It still does not exist.

The equation that applies here is the well-known F = ma.

F is gravitational attraction (= GMm/r2). It is a constant force, acting on this ball. You cannot remove that constant force.

And in nature, F = ma can also be written as F = m * dv/dt. That dv/dt term represents the change of velocity with respect to time. Calculus defines these dv or dt terms, or any others like these, as being infinitesimally small. So for example,

d(sin(t))/dt = cos(t). The differential of sin(t) with respect to time is cos(t). That cos(t) is a completely continuous curve, not some stepwise approximation. In nature, it's a continuous curve.

But how do we measure these phenomena? The measuring devices have to approximate. Instead of dv/dt, the practical, real world instrument must approximate this with delta v/delta t. Where "delta" represents a finite amount of time and finite change in velocity, so that the instrument can make practical measurements. So, whatever amount of time the instrument will claim the velocity was unchanged is an artifact. Not real.

Thanks Albert, I hear you; makes sense