How to explain that initial speed is zero? I was trying to discuss about free-fall with a friend, who is not scientifically literate. The first hurdle came quickly and unexpectedly as I was trying to demonstrate that the speed of free-fall is not constant : I hold a stone in my hand above the ground and let it fall. Since the stone is at rest initially, and visibly moving with a non-zero speed later on, that must mean that the speed varies along its trajectory, and therefore that it is not constant, right? Well, not really... My friend, a sceptic, did not find it obvious that the instantaneous speed is zero initially. I went on and demonstrated another way why the speed wasn't constant, but I found myself unable to explain (or rather demonstrate) the obvious about the initial speed... :( I must be missing something simple. 
Hence my question :
How can we demonstrate with simple words that the free-fall stone must be at rest initially, when it is let go? No maths please, only empirical proofs based on everyday observations. Thanks.
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I think I have something :
I hold the stone at a given height, h, ready to open my hand and let it fall. In parallel, I ask someone to take another, identical (same mass, same shape...), stone at the ground level and throw it in the air upward along a straight vertical line. Let's call this other stone the ref(erence) stone. But I ask the person one more thing : he should throw the stone with an initial force so that the ref stone trajectory apex, the highest points it reaches, is exactly h. We know that such an initial force exists and I think that no one can argue, even if he knows nothing about dynamics, that the ref stone has zero velocity at his apex.
As the ref stone reaches its apex, and the two stones are at the same level (by construction), I decide to open my hand, letting my stone fall freely. We can then notice that both stones reach the ground exactly at the same time. In fact we would also notice that at any given time the two falling stones remain at the same level. Another way to put it is that they fall at the same rate, which must mean that they have exactly the same speed along their downward trajectory, at any given time.
In particular, their speed must be identical at the beginning of their fall, as I open my hand. But we know (by construction) that the ref stone speed is precisely zero at its apex. That must mean the same for my stone at the beginning of its fall.
It's long but I think it works, and it does not require any strong prior knowledge of maths or of dynamics laws and concepts. It might not be the best way though, and I was hoping to find an example a bit less convoluted.
 A: Your friend is right to be skeptical. Of course, though, you are right.
What he should understand is that there is definitely a force being applied to it. However, it takes time, $t$, for this force to actually change anything.
1) First make him agree that you holding the rock  still makes the rock have 0 velociy or speed.
2) Then get him to understand that a force requires time for an object to be affected by it. If no time passes, the object does not move. For example, imaging taking a picture of a man hitting a baseball. There is clearly a force being applied to the ball, but the picture is not moving because there is no time.
3) At the instantaneous moment at which you release the rock, it must necessarily have the same resting speed at which you were holding it, 0. Only then is the force of gravity, which was being counteracted by your hand, able to move the rock.
I'm not quite certain how to explain it much simpler.
A: If your friend agrees that before, the rock is not moving with respect to your hand and that after, the rock is moving with respect to your hand, then your friend must agree that one of the following is the case
(1) the speed of the rock 'jumped' from to zero to non-zero the instant you released it or
(2) the speed of the rock smoothly increased from zero the moment you released it
If your friend is sceptical (and/or ignorant) of the scientific reasoning that argues for case (2), then perhaps your friend is open to the empirical evidence, e.g., high-speed photography, that (2) is the case.
If not, then don't waste another moment with your friend.
A: This is tricky! The best way I can think is to slow down time.
Without resorting to high speed photography you can do this with a smooth ramp and a billiard ball. Tilt the ramp just enough so the ball will roll. Now watch the motion carefully.
You could improve this experiment like Galileo did (IIRC). Add very small bumps to the ramp - fishing wire? - so the ball make a little sound. Now space the wires quadratically and note the the bumps are evenly spaced in time. Finally draw a picture of the bumps vs time and show you have made a parabola that is horizontal.
With the above you are slowly easing your friend into the mathematics of the situation without needing to ever invoke an equation. Pictures can work.
A: When rock is falling freely, it has constant acceleration due to gravity as it is falling under gravity. Now it is simple that if something is accelerating, that means it is speeding up which means speed is increasing
A: A visual demonstration.
Release a round object that roles down a gentle gradient.
It's velocity curve will be identical to the same object in free fall except that it is drawn out by the inverse of the gradient.
(I hope that makes sense)
That way you have more time to see what it happening.
