 Now, let's introduce the concept of instantaneous velocity. In general, velocity is how fast and what direction you're moving. Because of that, it's a vector quantity which has dimensions of type length over time and standard metric units of meters per second. Instantaneous velocity specifically means the velocity at a specific instant in time. This is compared to average velocity, which was over a time span, how did the velocity average out? Well, the instantaneous velocity is the default form. And so we often leave the word instantaneous off and just call it velocity. So the symbol for velocity is the vector lowercase v. And that is the instantaneous velocity or just called velocity. Now, when we did average velocity, we found that by taking the displacement divided by the time span. Or on a graph, we had two different data points that defined our time span. And we could find the slope connecting those two points to represent our time span and our displacement. For instantaneous velocity, we don't have two points to define something. We're dealing with a single point and you can't find the slope for a single point. Well, there's two different possibilities for how we're going to deal with this. If you have a simple graph where it's composed of line segments, each of which are straight sections, then we can deal with those. If you've got a plot where your position versus time is a curve, we're going to have to deal with that separately. Let's start with the straight sections because they're a little bit easier to understand. If I've got a straight segment, then along one particular whole segment, I always have the same slope. And that means I've got the same velocity along that whole segment because as I move up, I am continuously moving the same displacement in the same amount of time. So we can use the end points of that segment to help us calculate and find the slope. Here's an example. Let's say I wanted to find the velocity at a time of 1.5 seconds, which is on this first segment of the graph. Well, I can use the end points of that segment to help me define my time span and my displacement for that particular section of the graph. And in this case, that's a displacement of 6 meters and a time span of 3 seconds giving me 2 meters per second. So I've got 2 meters per second at a time of 1.5 seconds, but realize that I've got that exact same 2 meters per second when I've got 0.75 seconds or even 2.9 seconds. Anywhere along that segment, I have the same velocity of 2 meters per second. As a second example, we could look at a time of 7 seconds. Well, now I've got the segment over here is my straight line segment, so I want to use just that segment to define my time span and my displacement. In this case, we end up with a minus 1 meter per second for our velocity of that particular segment. And again, that applies for anywhere along the segment, 10 seconds, 8 seconds, 7 seconds, anywhere in there. My last example here is at 3.5 seconds. Well, I've got a straight segment there and I can easily define the time span of that segment, but you'll notice there's no displacement. I stayed at 7 meters that entire time. So what that means if I stayed at 7 meters for those full 2 seconds, I wasn't moving. I have a velocity of 0 meters per second. The slope of that section is 0. So whenever we have a horizontal segment, we know that the velocity anywhere along that segment is going to be 0. Now, if I've got curved segments, it's a little bit more complicated. What happens here is if I pick a particular time along that curved segment, I don't have a straight line endpoints to be able to define my slope. So instead, I want to use what we call the tangent to the curve, a line that meets that curve, which has the same slope for that particular point. So that tangent to the curve defines a slope. Once I've done that on my graph, I might be able to estimate from the graph what the slope of that tangent line is. Otherwise, if you want to calculate it exactly, you're going to need to use calculus to find the instantaneous velocity at a point along a curved segment. So this wraps up our introduction to the instantaneous velocity.