1 / 13

Algebraic Analysis of Motion: Five Principal Motion Variables

This article explains the five principal motion variables in algebraic analysis of motion and how to solve for them. It includes equations, examples, and tips for solving problems in physics.

sgibbs
Download Presentation

Algebraic Analysis of Motion: Five Principal Motion Variables

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. AlgebraicAnalysis of Motion

  2. Five principal motion variables • vo – initial velocity • vf – final velocity • Δx – displacement • a – acceleration • t - time

  3. Steps • If itis not given to youalready, define a positive direction • Make a chartgiving the values of the five principal motion variables. Include a sign for each one (except for time) • Whenthree out of the five variables are known, the remaining variables canbesolved for

  4. Physics 1 • Many times on the AP exam, thiswillbe all youneed to do, the question willasksomethinglike, isit possible to determine how much time the engineswere running? • Actuallydoing the math is a math skill, not a physicsskill. Even if calculations are called for, as long as they are reasonable (a model rocket burns for a few seconds, not thousands of seconds) youwillbeawarded full credit. • However, in class wewillbothwork quantitative and qualitative problemssoyou know how to do it all!

  5. The equations • Sometimes, youwillneed to use 2 of theseequationssothatyoudon’t have to solve a quadraticequation

  6. Example #1 Example:A boat moves slowly out of a marina (so as to not leave a wake) with a speed of 1.50 m/s. As soon as it passes the breakwater, leaving the marina, it throttles up and accelerates at 2.40 m/s/s. a) How fast is the boat moving after accelerating for 5 seconds? Define positive to be moving out of the marina Starting point is breakwater, ending point is 5 seconds later 13.5 m/s ALWAYS INCLUDE UNITS IN ANSWER!!!!

  7. Example #1 cont b) How far did the boat travel during that time? 37.5 m

  8. Does all this make sense? 13.5 m/s 1.5 m/s Total displacement = 7.50 + 30 = 37.5 m = Total AREA under the line.

  9. Example #2 Example:You are driving through town at 12 m/s when suddenly a ball rolls out in front of your car. You apply the brakes and begin decelerating at 3.5 m/s/s. How far do you travel before coming to a complete stop? Positive is direction you are moving Start of motion is when brakes are applied, end of motion is when you stop 20.57 m

  10. Example 3 Positive direction is direction plane is moving Beginning of motion is when the plane touches down, end of motion is when plane is stopped

  11. Example 4 Positive direction is direction spacecraft is moving Beginning of motion is when the retrorocket fires, end of motion is 215 km later (215000 m)

  12. Example 5 - qualitative • A bus driver makes an emergency stop by slamming on the brakes and skidding to a stop. How far would the bus have skidded if it had been traveling twice as fast? (in comparison to the 1st)

  13. Example 6 – Last one! A model rocket is launched straight upward with an initial speed of 50 m/s. It speeds up with a constant upward acceleration of 2.0 m/s2until the engine stops at an altitude of 150 m. How much time does it take for this to happen? Positive direction is up Beginning of motion is launch, end of motion is when engine stops

More Related