Water Fountain Fun

Last weekend, when I was getting a drink of water during a break in a meeting, I noticed that the more I pushed on the water fountain button/lever/whatever it's called that the water would shoot up higher. I'm sure that all of us have done this at one point in time, shooting water up our friends' noses when they asked us to hold the lever down for them. Back then, this was just a silly prank, but now that I'm in physics I can see that this is actually the work of velocity and gravity! The higher the velocity that the water is shot out of the fountain (the more push that is applied to the lever), the higher the water will shoot out (the higher the peak of its motion), and vice versa. The arc that's formed from the flow of water is due to the pull of gravity, the negative acceleration of all objects on earth (-9.8 m/s^2). At the peak of the three pictured arcs, the velocity of the flow of the water is 0 m/s because it's changing from positive to negative, however, it's still accelerating since its velocity is changing.
All objects thrown/catapulted/hurled/launched/etc. into the air without anything like a parachute or jet pack helping them to stay up will form arcs like those pictured above. Even professional atheletes who appear as though they're floating in the air when they jump are affected by the pull of gravity, accelerating back down to earth at -9.8 m/s^2.

Displacement, Velocity, and Acceleration

In these two photos, my friend Katie and I are running up a slight incline for a relay in Maui. As you can see, we have both positive displacement and velocity, as displacement is calcuated by finding the shortest path between the initial and final position of an object's motion (and taking into account the direction the object is traveling), and velocity is calculated by dividing the object's displacement by how fast it takes to move to that displacement. Since the displacement was positive, the velocity was also positive. Although our displacement and velocities were both positive, and we're traveling in a forward motion, we actually have negative acceleration, because we're slowing down as we're going forward. Acceleration is the change in instantaneous velocity dividided by elapsed time. Since our velocities in the second picture are lower than our velocities in the first picture, our accelerations are negative. However, if Katie and I happened to have been in better shape for the relay, we would have actually had positive acceleration and ran faster while going up the hill.
Another example of displacement, velocity, and acceleration in these two photos is the car that can be seen in the very back of the first photo and is the second car in the second photo. Its displacement and velocity are both positive, and one can easily see this by looking at its distance relative to the truck that was second to the last in the first photo and first in the second photo. The car also obviously has positive acceleration because of how quickly it moves from its position from way behind in the background of the first picture, to almost right behind the truck in the second picture.
Although Katie and I were slowing down while going up the hill, we must not have been going that slowly because the lady wearing the yellow remains behind us in the second picture. Perhaps she had the exact same negative acceleration!