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# Catalyst

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1. Catalyst • 1. What is the acceleration of an ant that begins crawling at 2 m/hr and speeds up to 3 m/hr in 1 hour? (Use the acceleration equation.) • 2. For a car that can go from 0 m/s to 100 m/s in 25 seconds, what would its final velocity be if it started from rest and accelerated for 10 seconds?

2. Today’s Agenda

3. Setting Up Your Graph • Position vs. Time Graphs • Distance on the vertical axis • Time on the horizontal axis • Label each axis • Make a scale for each axis

4. Analyzing Graphs • The slope of a graph is equal to rise/run which is equal to distance/time… the slope tells you your speed! • We can analyze graphs to get the instantaneous speed at certain intervals.

5. Position vs. Time Graphs • What can we get from this graph?

6. Position vs. Time Graph Demonstration • http://zonalandeducation.com/mstm/physics/mechanics/kinematics/xvaVsTime/xVsTime.html

7. Position vs. Time Graphs 1. Total displacement How? Find the starting position in meters, find the ending position in meters, and take the difference

8. Position vs. Time Graphs 2. Distance traveled during any time interval How? Pick your time interval, find the starting position in meters, find the ending position in meters, and take the difference

9. Position vs. Time Graphs 3. Total distance traveled How? Find the distance for all the line segments, then add

10. Position vs. Time Graphs 4. Time spent motionless How? Find all of the horizontal line segments (where slope is 0), find their lengths in seconds, then add

11. Position vs. Time Graphs 5. Instantaneous speed during any time interval How? Find the slope of the line segment using change in distance/change in time Steeper slope = greater speed

12. Analyzing Graphs

13. Analyzing Graphs

14. Today’s Agenda

15. Motion Graphs • There are THREE types: • Position vs. Time • Gives your position over a period of time. • Velocity vs. Time • Gives your speed (velocity) over a period of time. • Acceleration vs. Time • Gives your acceleration over a period of time.

16. Velocity vs. Time Graphs • These are new! • Slope is acceleration • Straight lines mean constant acceleration

17. Velocity vs. Time Graphs • Curved lines mean changingacceleration • Cannot find slope of curved lines

18. Velocity vs. Time Graphs • Horizontal (flat) lines mean no acceleration or constant speed

19. Velocity vs. Time Graph Demonstration • http://www.physicsclassroom.com/mmedia/kinema/fs.cfm

20. Acceleration vs. Time Graphs • Flat lines mean constant acceleration • Everything else means nothing! (for our purposes) • The only other acceleration vs. time graph you will see is this: • Which means no acceleration

21. Example: No Motion Position vs. Time Velocity vs. Time Acceleration vs. Time

22. Example: Constant Velocity Position vs. Time Velocity vs. Time Acceleration vs. Time

23. Example: Constant Acceleration = Object is Speeding Up Position vs. Time Velocity vs. Time Acceleration vs. Time

24. Today’s Agenda

25. Example + = ? B A

26. Example A B Use the tip-to-tail method to add your vectors. This means the tip (or head) of one vector (vector A) arrow meets the tail of the other vector arrow (vector B)

27. Example A B C Use the tip-to-tail method to add your vectors. Your resultant is the vector arrow that goes from the tail of A to the tip of B. Your resultant can be called Vector C.

28. Example + = ? B A

29. Example B A Use the tip-to-tail method to add your vectors. This means the tip (or head) of one vector (vector A) arrow meets the tail of the other vector arrow (vector B)

30. Example B A Use the tip-to-tail method to add your vectors. Your resultant is the vector arrow that goes from the tail of A to the tip of B. Your resultant can be called Vector C. Pythagorean Theorem!

31. Review: Pythagorean Theorem

32. Practice To complete the following problems, draw the vectors first and then add them to find the resultant and answer the problem. Add the velocities 15 m/s north + 6 m/s east. Add the velocities 10 m/s north + 5 m/s south. Find the resultant displacement if an ant walks 12 cm north and 8 cm west. Find the total velocity if Ricky runs 5 m/s east along a conveyor belt moving at 2 m/s east.

33. Today’s Agenda

34. More Kinematic Equations One example… • A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.5 m/s2. What is the velocity of the stroller after it has traveled 4.75 m?