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← 03-47 The Kinematic Equations

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Showing Revision 1 created 07/03/2012 by Amara Bot.

  1. This is our first serious equation of the course—Δx = V₀t + ½at².
  2. Now, I've introduced this Δ because this equation really describes how much
  3. and object position changes from here to there
  4. over a period of time, given an initial velocity and an acceleration.
  5. I wrote a here instead of g, because a is more general.
  6. In physics we like general equations.
  7. This is the acceleration of your object, which on earth in free fall does happen
  8. to be this number g, which is 10 m/s².
  9. On the moon, though, this number actually significantly smaller.
  10. So, this is one of the important kinematic equations.
  11. It's one of the equations that really describes how objects move.
  12. Now, there's a couple other kinematic equations that I want to talk about,
  13. and I'm actually going to do something that I'm a little reluctant to do.
  14. I'm going to give them to you.
  15. The next one I want to talk about is this one—
  16. velocity equals initial velocity + acceleration times the amount of time the object's been moving.
  17. Okay, fine. Why am I reluctant to give this to you?
  18. I'm reluctant because I already did.
  19. When we defined acceleration, we defined it as a change in velocity over some elapsed time,
  20. some change in time.
  21. In fact, that's exactly what this equation says, though it's hidden a bit.
  22. This velocity is actually what we can call some final velocity, after some time has elapsed.
  23. If we just rearrange this a little bit—like this—and then we can even divide by t if we'd like,
  24. we have this definition of acceleration.
  25. It's the change in velocity—final minus initial—over the elapsed time t.
  26. The last equation I want to talk about is this one. What does this one say?
  27. I says that there's some relationship between final velocity and initial velocity,
  28. acceleration and distance traveled.
  29. Deriving this one is a big trickier, but it's still something that I think you can do.
  30. I'm not going to do the derivation here, but I'd love to see some discussion about this in the forums.
  31. Now, let me say this is often the place where students get a bit scared.
  32. I've had many students tell me that equations are frightening,
  33. but the fact is they aren't. They're inanimate objects.
  34. They're not even objects. They're an inanimate idea.
  35. In fact, they're a tool. They're a tool for us.
  36. When you see a tool that you don't know how to use, you have two choices for how to respond.
  37. You can walk away, discouraged because you don't know what to do with it.
  38. Or you can imagine all the amazing things this tool will let you do,
  39. sit down, and learn to use it. I hope that's the option you choose.
  40. Let's sit down and learn how to use these tools.