A Mathematical Model of Motion

1. A Mathematical Model of Motion Chapter 5 Sections 1 and 2

2. Objectives Quiz 4 • Interpret graphs of position versus time for a moving object to determine the velocity of the object • Describe the information presented in graphs and draw graphs from descriptions of motion • Write equations that describe the position of an object moving at constant velocity

3. Objectives Quiz 4 • Determine from a graph of velocity versus time, the velocity of an object at a specified time • Interpret a v-t graph to find the time at which an object has a specific velocity • Calculate the displacement of an object from the area under a v-t curve

4. Position-Time Graphs • Shows where the object is at time intervals • X is time (Independent Variable) • Y is position (Dependent Variable) • Slope is velocity (Rise over Run, D over T) • No slope is no movement • Large slope is large velocity

5. Velocity Graphs • Show rate of change in position • When flat, constant velocity • When line falling, slowing down (or speeding up in reverse direction) • When line falling, speeding up • Area under graph is displacement

6. Acceleration Graphs • Show change in velocity • When line is straight, Constant acceleration • When line is flat, No Acceleration • When line is rising, increasing velocity • When line is falling, decreasing velocity

7. Connect • Slope of Distance-Time graph is velocity • Slope of Velocity-Time graph is acceleration • Derivatives

8. Graph A • What is the velocity of the object from 2 – 4 seconds?

9. Graph A • What is the average velocity of the object?

10. Graph A • At what time's does the object have a negative acceleration?

11. Graph A • At what time is the object located at 11 m? • How many significant digits?

12. Draw a Position-Time Graph • A man • walks at a constant velocity of 2.0 m/s for 5 seconds. • The man stops for 3 seconds. • The man resumes his walk but walks slower at 1.0 m/s for 5 seconds

14. Draw a Position-Time Graph • A Dragster in a race

15. Interpreting Graphs • On the following slides, describe the motion of the object • What real life event could the graph be showing?

20. Nothing in Mind

21. Long Jump (Horizontal speed)

22. Jump (Vertical Position)

23. Baseball Pitch (Horizontal)

24. How fast was pitch?

25. How fast was hit?

26. If the jumper jumped at 2 s, how far did they jump?

27. Velocity-Time Graphs • Shows objects velocity at time intervals • Y is Velocity • X is Time • No slope is constant speed • Positive slope is Positive acceleration • Large slope is large acceleration

28. Graph B • Total Displacement?

29. Graph B • Average Velocity?

30. Graph C Greatest Acceleration is where?

31. Graph C • Average Velocity?

32. Graph C • Total Displacement?

33. Graph D • Total Distance Covered?

34. Graph D • Average Velocity?

35. Graph D • Acceleration at different parts of graph?

36. For the next slides, determine what the acceleration is • For the next slides, determine how far the object was displaced • Area under graph is displacement

37. Velocity vs Time

38. Velocity vs Time

39. Distance vs Time

40. Draw a D-T and V-T graph from situation described • A car is driving down the road at 55 mph and gets a flat tire. The car slows down to a stop. The driver changes the tire and then continues driving and moves at 35 mph.

41. Draw a D-T and V-T graph from situation described • A bullet is fired from a gun and travels 1000 meters in one second before hitting a solid target.

42. Draw a D-T and V-T graph from situation described • At basketball practice, coach has you run the down and backs the length of the court. You do 3 down and backs with each trip taking slightly longer than the last

43. Position Time • Fastest object? • Stopped object? • Negative velocity? • Accel?

44. Velocity Time (mid line 0, above positive) • Slowest? • Fastest? • Stopped? • + Accel • - Accel