1. Kinematics (Stuff moving) (stuff)

2. Start with vocabulary Position (x)– where it is (meters) Displacement (  x)– how far it moved, direction (+/-) is important (meters) Velocity – (v) how fast it moves, direction is important (+/-) (meters/second) –Instantaneous, right now! Slope of tangent Average velocity – change in position divided by change in time

3. Vocabulary, continued Acceleration (a) – rate of change in velocity –m/s 2 –Instantaneous, Slope of velocity time curve –Average, over time interval –Our equations apply only to constant acceleration –When acceleration changes, we break the problem into chunks of constant acceleration

4. The Equations! All you get on AP Equations Sheet Don’t forget these definitions!

5. Daddy

6. Mommy Notice no time in this one!

7. The area of a velocity “curve” is displacement! v t Avg velocity area

8. Tips for deciphering word problems …at rest, …from rest – not moving at beginning… v 0 = zero!..comes to rest… v f =zero …Travels 10 m in 10 sec… –  x=10m,  t=10 s …reaches a maximum height – velocity at h max = zero!

9. The Equations!

10. Kinematics Examples Drag race –Avg velocity given time and disp –Avg acceleration given final v and disp Motion Graphing –Aircraft Catapult Draw position and acceleration given velocity

11. Drag Race 1. A car travels 402.34 meters in 11.963 sec. What is its average velocity? 2. The same car reached 40.73 m/s at the end of the first 201.17 meters. What was its average acceleration?

12. Drag Race #1 Unknown: v avg =?? Given:  x= 402.34 meters in  t=11.963 sec. Principle: Kinematics(where to look for eq’n) Equation: Picture: Simplify/Solve/Substitute

13. Drag Race #2 Unknown: a avg =?? Given: v f = 40.73 m/s in  x=201.17m Principle: Kinematics(where to look for eq’n) Equation: Picture: Simplify/Solve/Substitute zero

14. Aircraft catapult Navy aircraft are launched from the decks of aircraft carriers with a steam powered catapult. The graph shows the velocity of the aircraft as a function of time. Analyze the graph and draw corresponding position and acceleration graphs.

15. Aircraft Catapult(v) 50 v(m/s) time(s) 5

16. Aircraft Catapult(a) 20 a(m/s 2 ) time(s) 5

17. Aircraft Catapult(x) x(m) time(s) 100 5 300 200

18. Freefall Same kinematics equations… Just constant acceleration of a=g=9.8 m/s 2 toward earth. Do yourself a favor and call down negative.

19. 1) A ball is dropped from 10 meters high. –A)How fast is it going when it hits the ground? –B) How long does it take to reach the ground? Freefall Example

20. 2) A ball is given an upward velocity of 5.0 m/s, what is the maximum height it will reach? 3) How long does it take to reach this max height? Freefall Example

21. 5) A ball is thrown upward with a velocity of 4.0 m/s. How fast is it going when it hits the ground, 10 meters below where it was thrown from? Freefall Example

22. Freefall Cases Downy –Dropping or “spiking” Uppy –Toss up Uppy – downy –Toss up off a ledge, object lands lower than the ledge Establish your coordinate system and be consistent with signs.

23. Wrap up Givens Unknowns P&P E –Time or none given S & S & S

24. More examples More example problems Try: v 0 =-3.0, a=5,  t=4,  x=? Try a “spike” (as in football player’s touchdown celebration) –x f =-5.0, x 0 =2.0, v 0 =-1.0, a=-9.8,  t=?

25. The Equations! Don’t forget definitions

26. Drag Race #1 Unknown: v avg =?? Given:  x= 402.34 meters in  t=11.963 sec. Principle: Kinematics(where to look for eq’n) Equation: Picture: Simplify/Solve/Substitute

27. Drag Race #2 Unknown: a avg =?? Given: v f = 40.73 m/s in  x=201.17m Principle: Kinematics(where to look for eq’n) Equation: Picture: Simplify/Solve/Substitute

28. Aircraft Catapult(v) 50 v(m/s) time(s) 5

29. Aircraft Catapult(a) 20 a(m/s 2 ) time(s) 5

30. Aircraft Catapult(x) x(m) time(s) 100 5 300 200

31. 1) A ball is dropped from 10 meters high. –A)How fast is it going when it hits the ground? –B) How long does it take to reach the ground? Freefall Example

32. 3) A ball is given an upward velocity of 5.0 m/s, what is the maximum height it will reach? 4) How long does it take to reach this max height? Freefall Example

33. 5) A ball is thrown upward with a velocity of 4.0 m/s. How fast is it going when it hits the ground, 10 meters below where it was thrown from? Freefall Example