Hey it's professor Dave, let's discuss position, velocity, and acceleration. In physics, we will often be asking questions like where is an object, which way is it moving, and how fast? To discuss the answers to these questions we will frequently utilize the concepts of position, velocity, and acceleration. So before we go any further let's define these terms. Position is simple, it's just where an object is in space. Usually this is discussed with some kind of reference point or axes in mind, and we might express the position of an object as being some distance from this reference point in meters. Velocity is the change in position over time, so if this object travels five meters in five seconds it is traveling at a velocity of one meter per second. And acceleration is the change in velocity over time, so if this object starts at a standstill and over five seconds gradually speeds up to 5 meters per second, then it is accelerating at one meter per second per second, or 1 meter per second squared. So that's how we define position, velocity, and acceleration. Now let's discuss each of these in more depth. When we talk about position we could discuss distance or we could discuss displacement. The difference here is that distance is a scalar while displacement is a vector. Let's say you and your friend get dropped off by the school bus at this intersection and your house is here. Your friend begins to walk down the street and up the driveway like a normal person but you find yourself so overcome with excitement to play video games that you decide to plow through the yard in a straight line to the door. Your friend has to walk 20 meters down the street and seven meters up the driveway for a total of twenty seven meters, so using the Pythagorean theorem we find that you only had to walk about 21.2 meters and you probably got there a little sooner. What we can say is that you walked different distances, which are represented by these scalar values, but you both had the same displacement because you ended up in the same spot at the front door. This vector which follows the straight-line path is the displacement vector for both of you and we can report your position with x and y-coordinates like this (20, 7) or we could report the magnitude of the displacement vector which will be equal to the shorter distance you traveled and calculate the angle off the horizontal using trig functions if we desire, in order to report the direction of the vector. Next let's look at velocity which is the rate of change in position. Most people assume that the words speed and velocity are synonyms and in everyday language they are, but the difference in physics is that speed is a scalar and velocity is a vector. If a group of kids are playing hide-and-seek and they all run away from the seeker in different directions it is possible that they all run at the same speed because speed only has magnitude and no direction so they could all run at a speed of three meters per second if they are quick little devils but each kid would have a unique velocity vector that has a magnitude of three but also describes the direction of motion, most likely using the seeker standing still as the point of origin. Velocity vectors will be extremely important as we move forward with kinematics where we will study the motion of objects. In general, average speed can be calculated by taking the distance travelled by an object and dividing by the time it took to do so, so if you walk 85 meters in 46 seconds you are walking at an average speed of 1.85 meters per second. To find average velocity you can do the same but you would have to divide displacement by time. Lastly we have acceleration, which is the rate of change in velocity. This is always a vector, because acceleration must occur in a particular direction. If you are in a car that is standing still and you press on the gas, the car will begin to move forward with a fixed acceleration. It might accelerate slowly so the vector may be on the shorter side, but this constant acceleration will cause the velocity to increase at a fixed rate, let's say an additional meter per second every second, so over five seconds it will reach a velocity of 5 m/s. Let's say you see a skunk in the middle of the road. It's your most favorite animal so you slam on the brakes. We can describe this as a deceleration, which is an acceleration in the negative direction. Since you are going from a moderate speed to a standstill in a very short amount of time this vector will be quite long and pointing back towards the origin. Now we understand distance and displacement, speed and velocity, and acceleration, and we can categorize these as being either scalars or vectors. Before we finish let's look at a moving object like this marble rolling to a stop and visualize all three of these vectors as the object moves. First with displacement this vector will just elongate as the marble rolls and will span the distance travelled. For velocity the vector will point forward as the velocity is positive, since it is moving in the forward direction, and the vector will move along with the marble but it will decrease in magnitude as the marble slows down until eventually disappearing when the marble comes to a rest, where it has zero velocity. And then for acceleration the vector points in the negative direction since velocity is decreasing or becoming smaller per unit time but it will be constant in magnitude since this is a constant deceleration due to friction from the surface it's rolling on. We can view all three of these at once just to drive things home. Make sure you understand the magnitude and direction of each of these vectors at each moment in time. Let's check comprehension. Thanks for watching, guys. Subscribe to my channel for more tutorials, support me on patreon so I can keep making content, and as always, feel free to email me: