Question: I was once asked the following question by a student I was tutoring; and I was stumped by it:

When one throws a stone why does it take the same amount of time for a stone to rise to its peak and then down to the ground?

* One could say that this is an experimental observation; after one could envisage, hypothetically, where this is not the case.
* One could say that the curve that the stone describes is a parabola; and the two halves are symmetric around the perpendicular line through its apex. But surely the description of the motion of a projectile as a parabola was the outcome of observation; and even if it moves along a parabola, it may (putting observation aside) move along it with its descent speed different from its ascent; or varying; and this, in part, leads to the observation or is justified by the Newtons description of time - it flows equably everywhere.
* It's because of the nature of the force. It's independent of the motion of the stone.

I prefer the last explanation - but is it true? And is this the best explanation?

Answer: 
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> One could say that this is an experimental observation; after one could envisage, hypothetically, where this is not the case.
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This is not hypothetical once you take air resistance into account.

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> One could say that the curve that the stone describes is a parabola; and the two halves are symmetric around the perpendicular line through its apex. But surely the description of the motion of a projectile as a parabola was the outcome of observation; and even if it moves along a parabola, it may (putting observation aside) move along it with its descent speed different from its ascent.
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> 
> 

Assuming constant horizontal velocity, the height vs time diagram will essentially look the same as the height vs horizontal distance diagram. Under that assumption, it is valid to argue about time-of-flight from the symmetry of the trajectory; in general, it's not.

> 
> It's because of the nature of the force. It's independent of the motion of the stone.
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The motion of the stone depends on the force, so it's hardly independent.

Under constant vertical acceleration, the change in vertical velocity is linear in time. This means that it takes the same amount of time to go from initial velocity $+v$ to 0 as it takes going from 0 to $-v$. In fact, the velocity profiles will be mirror images, and the same distance will have been covered.
Asking "Why" in physics often leads out of physics and into philosophy. Why is there light? Because God said so. Physics only answers questions about how the universe behaves and how to describe that behavior. If a why question can be answered with physics, the answer is "because it follows from a law of physics." A law is just a mathematical description of behavior that has been verified with experiments. 

In this case, the answer follows from $F = ma$. If $a$ is constant, this leads to $x = 1/2at^2 + v\_0t + x\_0$. Since you are a physics tutor, you can set up the initial and final conditions and solve for t. 

This may well lead to more questions. Why is $F = ma$? Why is there gravity? You could fall back on philosophy, or you could say "I don't know. But experiments show that it works this way."

Why questions are usually about things that are unfamiliar. A young child will ask "Why is there gravity?" A high school student is more likely to ask "Why is $F = ma$?" He may not know the answer to the first question, but he has become used to it. 

So the way to answer $F = ma$ questions is to show how it applies to familiar situations. This is why high school physics is full of pictures of springs and ropes and pulleys.