Kinematics Part 1: Horizontal Motion

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:

100 thoughts on “Kinematics Part 1: Horizontal Motion

  1. I don't understand why at 5:25 it's
    x = 86 – 43

    Where does the 43 come from?

    0.5(-8.4)(3.2) gives me -13.44.

    Thanks and I appreciate your videos.

  2. Man, you're such a great teacher and I pray God increases you in knowledge even more. Thank you, from your muslim brother.

  3. David… You would be powerful beyond any Jedi, if you lost the theme at the start and end.

  4. after acing the chemistry test a while ago, time to finish up the finals with physics, thanks a lot for helping me Jesus!

  5. wow, this was a great video. So basically we have to find out first what we have and what we need to find out in order to know which equation we have to use? The first day of Physics was so confusing and now that we're on the 3 chapter (Freefalling​) we have an exam on the first 3 chapters but I still feel somewhat lost. I'm gonna have to watch videos and apply it to what I'm reading to get a better understanding.

  6. thanks professor dave. ur great. u make physics fun. also, i rly like ur ending song. it brings me pure happiness. pls b my friend.

  7. Hi professor! You are helping lots of people improve themselves and most likely their spheres, thanks a lot for that!!

    I just wonder why the time we plug into the 2nd monomial (Vi*y) of the second ecuation isn't the time in which that initial velocity took place. It makes sense to me that in the "1/2 at" part it refers to the time that accelerations takes place but what about that other part?

    I understand that "t" should have a constant value in the same problem, but how was it determined that it is the time the acceleration takes place rather than the time the inicial velocity did?

    Hope this makes sense to anyone 🤔🤯😵😁

  8. I am not understanding how the equation went from (27 m/s) + (-8.4 m/s squared) t.. To you dividing the two variable also not sure how you where able to change 27 to a negative and what happened to the square??? also in the other equation( xt =xo + v, t +1/2 at squared) simplifed too ( xt =1/2 at squared what happened to the time + 1/2 ???

  9. This is awesome but I have a question in the second example why did you not consider the initial Position Xo in the formula Xt = Xo + Vit +1/2 a*tsqr is it because the vehicle is already in a motion for a long time and considering the origin is irrelevant for us to obtain the solution.

  10. I dont get it. If the car is moving ONLY horizonta3, arent you supposed to only use the horizontal component formulas? And therefore not using the vertical(free fall) compinents

  11. 3:28 these weren’t equations used in the beginning of the video. How am i supposed to know to solve anything with these equations

  12. Our physics teacher shows your videos during class but I always have something to do thats why Im distracted every class but when i go home i watch ur videos again and I understand the lesson. Thank you!!

  13. Hey Dave amazing tutorials very helpfull and entertaining! I just didn't get how -27m/s=(-8,4m/s)t come to t=-27m/s ÷ -8,4m/s can you break it down?

  14. can someone help me out. if in kinematics the acceleration is constant then does that mean that acceleration equals velocity? or is acceleration 0 and velocity is a constant number?

  15. I hate it when teachers tell you a formula and then dont derive it and just say magic! Like how did Galileo find these formulas and etc ?

  16. Hey Proffy Dave, I have a question…When I am getting more into physics I see a lot of talk about "Deriving an equation"…or something like "Derive the kinematic equations" etc… Is this the same meaning as literally taking the derivative of the equation? Or does "deriving" in this sense mean something else? From what i see…when someone says they "Derive an equation" it doesn't seem like the same idea as taking the derivative of a function or equation? How are they releated/different?

  17. At 5:17 there is a farting noise in the background for some reason, start a few seconds early (such as 5:15) to find it properly.😅

  18. Pardon my ignorance but I'm a little confused with some of the questions and formulas.

    During the first example

    It is mentioned that velocity = 25 m/s but wouldn't that be the traveled distance or the total displacement of the car? Well, 25 m not m/s. Isn't distance = speed * time? 25 m/s seems too high if it only moved for 10 seconds and the traveled distance was 25 m. I might be wrong.

  19. I am so thankful for you! I was getting so frustrated and now I feel hopeful. Thank you for breaking things down in a simple manner!!

  20. Heyzues Christopher, I just sat through a three motion two object kinematic problem and this 4 part video series has been a huge asset in getting this information to stick. Many thanks!

  21. You helped me pass genetics and O. chem the second time around. Now here I am drowning in physics and I find out you teach that too… BLESS YOU PROFESSOR DAVE :')

  22. My question is after you are done with these and rounding to appropriate sig figs, do you use the 2 used as part of the formula or only the measurements in the equation to calculate how many sig figs should be in your answer? My teacher is confusing me on that part.

  23. I just wanted to take the time to genuinely thank you sincerely. For the past 2 weeks in my physics class I have been extremely lost, and your video helped me apprehend the necessary conceptions. Thank you so much.

  24. There's also a method where you plot a graph with the x axis being time and y axis being velocity, the area of the polygon in the graph is the displacement of the time, velocity and acceleration of the problem.

  25. Why are you using d here for displacement? D was already the scalar distance so s for spatia was chosen for displacement.

  26. If given the answer for the latter problem, is it able to be said that it would take the person 22.2 seconds to stop fully?

  27. thank you SOOO much for making this. I've been struggling with kinematics really badly in class, and this explained it in such an easy and understandable way

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