 Now let's take a look at the effect of different initial velocities on what we see for a free fall problem. Quick reminder that free fall is where the acceleration is due to gravity and that's a 9.8 meters per second downward if we're anywhere near the surface of the earth. And this is a special case of constant acceleration because it always has that value of 9.8 meters per second downward. If we look at it in formulas our constant acceleration for the y direction can be written out in this form and plugging in our acceleration that gives us these forms of the equations. But the initial velocity and the time are still in there to find your vertical displacement or your vertical final velocity as you're moving through time. Now when we look at our initial velocity and our introduction we only covered starting from rest or if you just let go or drop something. But you could also start moving upwards and this is where your initial velocity is any positive number and think about it if you toss something up in the air as soon as it leaves your hand it's got an upward velocity or you could toss it downwards which means the initial velocity as soon as you let go of it is some negative number. We've already looked at starting from rest and our introduction and just as a reminder I start and I fall and if I actually calculate that out that gives me my quadratic path or my dots that are becoming further and further spaced apart. And we saw that in terms of velocity this means that I start up here at pretty much zero velocity my dots are almost on top of each other and that velocity moving downwards is increasing in speed meaning I'm moving to more and more negative numbers and that gives me a straight line with a slope of minus 9.8 meters per second squared which is our constant acceleration. Now let's talk about moving upwards. If I throw something up in the air just thinking about what happens it's going to start moving upwards eventually is going to reach some sort of place where it then turns around and starts falling. Plugging this into the equations my position versus time graph still shows me a quadratic but now I've got the upward part of the quadratic before it starts to fall down. When I translate this kind of position plot over into my dot motion diagram I separate out just a little bit to the side the upward part and the downward part and that's just so the dots aren't right on top of each other and I can see what's happening. If I look at the velocity for this sort of a graph what I see is I start moving upwards but that the size of the little spacing comes to zero as I get to the very top and then it starts from zero and again gradually picks up negative speed moving downwards just like the dropped from rest case. If I plot this out as my velocity versus time graph I see then that I'm starting at a positive velocity value but that the velocity is dropping as I slow down until I reach that point where it stopped just momentarily at the top but then it continues right back down moving downwards. So it's still a straight line with a slope of minus 9.8 meters per second squared showing us that the acceleration is constant over that entire range. That special value at the top is just where it crosses from being a positive velocity to being a negative velocity right up here at that maximum height. If I'm moving downwards as I throw it well it's just going to fall straight downwards. Plotting it out what I see here is I'm again starting from that same height falling down which I can translate into my dot diagram over here and I look at the velocities I see that I don't have those two dots right on top of each other to start with. So when I look at my velocities that means my very first point here is actually already a negative number my initial negative velocity and that continues to grow as I move over time to more and more negative velocity values but just like our previous two cases I still have a slope of minus 9.8 meters per second squared. I can really learn a lot if I start comparing these graphs. So here I've got my three cases where I start from rest, start moving upwards or start moving downwards as they're labeled here. For the position graph all three of these are showing a quadratic with time but following slightly different paths with the one which was moving upwards having the upward part of the curve before it started sloping downwards. Now remember these aren't moving off towards the side as they're falling this is the time so what this tells us is that it takes a lot more time to go all the way up and back down than if I just dropped it and if I throw it downwards it moves even faster towards the ground. When I compare the three velocity graphs it's really really obvious that all three cases have a constant acceleration with a slope of minus 9.8 meters per second squared. Acceleration is always constant in free fall and we know that value. The only difference is where it starts and if it starts above the line you can find that maximum height is when it's going to cross that zero axis. So that wraps up the initial velocity effect on free fall. We're going to look at a lot more examples as you're going.