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How To Go Nowhere Fast…

How To Go Nowhere Fast…. Displacement, Velocity and Acceleration. More Trig…. Pythagorean Theorem To find an angle, you need the inverse trig function i.e. x = y = 1 What is r? ?. Dynamics & Kinematics. Dynamics is the study of motion and of physical concepts

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How To Go Nowhere Fast…

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  1. How To Go Nowhere Fast… Displacement, Velocity and Acceleration

  2. More Trig… • Pythagorean Theorem • To find an angle, you need the inverse trig function • i.e. x = y = 1 What is r? ?

  3. Dynamics & Kinematics • Dynamics is the study of motion and of physical concepts (i.e. relationship between force and mass) • Kinematics is a part of dynamics • description of motion • Not concerned with the cause of the motion

  4. Quantities in Motion • Any motion involves three concepts • Displacement • Velocity • Acceleration • These concepts can be used to study objects in motion

  5. Section 1.1:Displacement • Defined as the change in position • f stands for final • i stands for initial • SI units are meters (m) Displacement vs. Time graph

  6. Displacement vs. Distance Displacement is NOT the same as Distance i.e. Throw a ball straight up and then catch it at the same point you released it • The distance is twice the height • The displacement is zero

  7. Vector & Scalar Quantities Vector • has magnitude & direction i.e. - instantaneous velocity - instantaneous acceleration Scalar • has magnitude only (v, t, mass)

  8. Section 1.2:Speed Speed the totaldistance traveled divided by the total time elapsed • Speed is a scalar quantity • Average speed completely ignores any variations in the object’s actual motion

  9. Average Velocity… Velocity is therate of change of displacement per unit time Units? Slope is velocity!!!

  10. Speed vs. Velocity Cars on both paths have the same average velocity… Why? • … they have the same displacement (in the same time interval). The car on the blue path will have a greater average speed…Why? • … the distance it travels is larger (in the same time interval)!

  11. Position vs. Time Graphs What will the position vs. time graph look like for the following: • Stand still • Slow steady walk • Fast steady walk • How should I move to reproduce the graph on the previous slide?

  12. Interactive Position Time Graph • Stand still • Slow steady walk • Fast steady walk

  13. Acceleration • the rate of change in velocity per unit time (v/ t) • Units?

  14. Graphical Interpretation of Average Acceleration • Average acceleration equals the slope of the line joining the initial and final velocities (vs. time)

  15. Graphical Interpretation of Velocity • Average velocity equals the slope of the line joining the initial and final positions (vs. time) A – start at 30m from start and decelerate (neg. acceleration) to B B – Velocity is 0 m/s Start to accelerate in reverse C – Constant velocity in reverse. D – At start position. Continue in reverse at constant velocity E – Begin to accelerate in forward direction (slow down in reverse). Stop at F.

  16. 1-D Vector Problem Two boats start together and race across a 60-km-wide lake and back. Boat A goes across at 60 km/h. Boat B goes across at 30 km/h, and its crew, realizing how far behind it is getting, returns at 90 km/h. Turnaround times are negligible, and the boat that completes the round trip wins. • Which boat wins and by how much? (Or is it a tie)? • What is the average velocity of the winning boat?

  17. Quick Quiz… • Match each velocity vs. time graph to its corresponding acceleration vs. time graph.

  18. Section 2.4: Motion Diagrams (Relationship between a and v) • Uniform velocity What is the acceleration? • a = 0

  19. Relationship Between a and v • v and a are in the same direction • a is constant • v is increasing

  20. Relationship Between a and v • v and a are in opposite directions • a is constant • v is decreasing

  21. 1. Which car or cars (red, green, and/or blue) are undergoing an acceleration? Study each car individually in order to determine the answer. Red car – moves at a constant velocity Green Car – accelerates Blue Car - accelerates

  22. 2. Which car (red, green, or blue) experiences the greatest acceleration? Blue Car – Has the greatest acceleration Green Car – Has the 2nd greatest acceleration Red car – does not accelerate

  23. 3. Match the appropriate line to the particular color of car. Blue Car Red car Green Car

  24. Acceleration in Motion

  25. Animated Car Graphsdvs. t v vs.t a vs. t

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