It's professor Dave, let's talk about horizontal motion. As we learn classical physics, a big topic of study will be mechanics. This is a branch of physics that can be divided into two smaller topics: kinematics and dynamics. Kinematics, which was developed largely by Galileo in the early 1600s, deals with equations that describe the motion of objects without reference to forces of any kind, whereas dynamics is the study of the effect that forces have on the motion of objects. These topics together comprise mechanics. We are going to focus on kinematics over the next few tutorials so that we can familiarize ourselves with the ways that simple equations will govern the motion of objects in one and two dimensions. These equations are revolutionary, because from Aristotle until Galileo we thought that mathematics could only describe the perfect motion of divine celestial objects, and that the motion of objects on earth was too imperfect and unpredictable to calculate. But we soon found that the same equations governing the motion of all objects, whether on earth or in space, it is simply that on earth we must make approximations since there are a greater number of variables like friction and atmosphere that affect motion in various ways. The kinematic equations include variables for displacement, velocity, acceleration, and time, and in the context of kinematics acceleration will always have a constant value, whether positive, negative, or zero, since we won't look at forces that could cause acceleration to change over time. When you see a subscript of zero after velocity or displacement it indicates initial conditions which will have some implication depending on the problem we are looking at. Here are the three fundamental kinematic equations we will be using. The first one says that the velocity of an object at any time T is equal to the initial velocity plus the acceleration times time. The next one says that the position of an object with respect to a point of origin will be equal to its initial position plus the initial velocity times time plus one-half the acceleration times x squared. Lastly, this one says that velocity squared is equal to the initial velocity squared plus twice the acceleration times the displacement. Other supplemental equations include these two, which are easily derived from simple definitions, which state that position is equal to the average velocity times the time interval and that the average velocity is equal to final velocity plus initial velocity over 2, which is the definition for any average. Now that we have these equations and know what all the variables mean, we are ready to apply them to real examples of motion. Say you get in your car to drive to the supermarket. While at rest, you place your foot on the gas and apply a constant acceleration of 2.5 meters per second squared. What will your velocity be after 10 seconds and how far will you have traveled in that time? We can use these two equations to find the answers, we just have to plug in what we know. For the velocity, we know that the initial velocity was zero because we were at rest, so we just multiply acceleration by time and we get 25 meters per second. That is the velocity of the car after 10 seconds. Now to find how far you will have traveled, you will use this equation. Once again, initial velocity is 0 so this entire term can be ignored. Then we have one-half times the acceleration times 10 seconds squared and we should get a hundred and twenty-five meters traveled over this time span. So it really is this simple. You just choose the equation that is appropriate for what you are solving for and plug in what you know. Let's now consider a car that is already in motion with a velocity of 27 meters per second. Let's say you need to stop suddenly so you press on the brakes, initiating a rapid deceleration of -8.4 meters per second squared. How long will it take the car to come to a stop and how far will it travel while your foot is on the brake? Once again let's use this equation to solve for time. It must be this equation because we know everything in it except for time. For velocity let's plug in 0 because we are curious about the time elapsed at the moment that the car stops moving, and the velocity when it has stopped moving will be 0. The initial velocity is the 27 meters per second we mentioned, and we can plug in the acceleration, solve for time, and get 3.2 seconds. Now that we know the time associated with this event we can use this other equation to find the braking distance. We plug in the initial velocity and acceleration we mentioned before, as well as the 3.2 seconds we just calculated, and solve for x which will be about 43 meters traveled from the moment you applied the brakes to the moment that the car stops moving. These equations work for any other object just as they do for cars so 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: