2. 1.Measurements & units 2.Scalars & vectors 3.Displacement, Velocity and acceleration 4.Relative velocity. 5.Motion in two dimensions and in three dimensions 6.Special case: Gravity

3. Summary Vectors: Positions, Displacement, Velocity and Acceleration.

4. Vector or Scalar? Speed……….. Velocity……... Acceleration.. Time…………. Force………… Distance…….. scalar vector scalar it depends...

5. Some Derivatives Powers Trig Functions Exponentials

6. Average Velocity What is the average velocity in the last second (t = 3 to 4) ? A. 2 m/s B. 4 m/s C. 1 m/s D. 0 m/s x (meters) t (seconds) 2 6 -2 4 1243

7. Instantaneous velocity What is the instantaneous velocity in the last second? A.-2 m/s B. 4 m/s C. 1 m/s D. 0 m/s x (meters) t (seconds) 2 6 -2 4 1243

8. Average Speed What is the average speed over the first 4 seconds ? A. 2 m/s B. 4 m/s C. 1,5 m/s D. 0 m/s x (meters) t (seconds) 2 6 -2 4 1243 turning point

9. Correcting home exercises What is displacement of a train from staring point to point at 3 seconds after ? What is the velocity and acceleration of a train ?? (AV or IV) from staring point to point at 3 seconds after ?

11. Part 4 Relative velocity.

12. Air speed Ground speed Brainstorming

15. Galilean formula of velocity sum

16. Learning Check

17. Solution a) Up

18. Learning Check ground river boat

20. Part 5 Motion in one dimension and in two dimensions

21. Linear motion

24. 0 is certain point Green car with solar cell

25. Learning Check John is moving to x direction by equation: X= - 25t 2 +3t +7 (cm) 1- What is John ‘s position at time t=0? and t = 3(s) ? 2- What is his velocity at time time t=0? and t = 3(s) ? Average speed of John after 10s moving? 3- What is his acceleration at time time t=0? and t = 3(s) ? Average acceleration of John after 10s moving?

26. Learning check Acceleration vs Time Plots Gives acceleration at any time. Area gives change in velocity Acceleration at t=4, a(4) = Change of v between t=4 and t=1.  v = a t 4 3 -3

28. Constant Acceleration Equation of motion is The o in v subscript refers to the original or initial value at the beginning of the time interval of interest. Integrate both sides where acceleration is constant. Solution

29. Arranging this equation Substituting the velocity equation from the previous page Integrating both sides

30. Learning Check X=2+10t +4t 2 (m) At t=3  x= 2+3.10 +4.9 = 68 (m) V= 10 + 8t (m/s) At x=4  4= 2+10t +4t 2  4t 2 +10t –2 =0  t = ?

31. Part 5 Motion in two dimensions

33. Positions in 2 dimensions

35. Where is velocity zero? Where is velocity positive? Where is velocity negative? Where is speed largest? Where is acceleration zero? Where is acceleration positive? position vs. time velocity vs. time Example

36. Learning Check

39. Part 6 Free fall Isaac Newton in 1689, by Sir Godfrey Kneller.

43. History

48. Learning Check

49. Exercises of today’s lecture A ball is thrown straight up in the air and returns to its initial position. During the time the ball is in the air, which of the following statements is true? A - Both average acceleration and average velocity are zero. B - Average acceleration is zero but average velocity is not zero. C - Average velocity is zero but average acceleration is not zero. D - Neither average acceleration nor average velocity are zero.

50. Summary of Concepts kinematics: A description of motion position: your coordinates displacement:  x = change of position velocity: rate of change of position –average :  x/  t –instantaneous: slope of x vs. t acceleration: rate of change of velocity –average:  v/  t –instantaneous: slope of v vs. t

51. Class Question How do units differ from variables? List 10 clear examples of units and 10 clear examples of variables.

52. Problem A motorcycle moves with an initial velocity of 30m/s. When its brakes are applied, it decelerates at 5.0m/s 2 until it stops. Plot the position, velocity and acceleration as a function of time. What is the position, velocity and acceleration 2 seconds after the brakes are applied? Use bike computer

53. Bikebrain Source: http://www.bikebrain.com Attaches to a “PalmPilot”

54. Problem A car starts from rest and travels northward. It accelerates at a constant rate for 30 seconds until it reaches a velocity of 55mph. Plot the acceleration, velocity and position as a function of time.

55. Problem A girl shoots an arrow upward. It strikes the ground 10.0 seconds later. What was its initial velocity and what was the maximum height?

56. Problem A man standing on a 20-m helicopter throws a ball upward at 120 m/s. How long does it take to hit the ground?

57. Team Exercise, 3 min. 1.The derivative of velocity with respect to time is: –position or acceleration 2.By integrating velocity with respect to time we get: –distance traveled or acceleration 3.The derivative of position with respect to time is: –acceleration or velocity 4.Integrating acceleration twice with respect to time is : –velocity squared or distance 5.The derivative is associated with the _________ while the integral is associated with _________ –area under the curve, slope

58. Team Exercise (3 minutes) One dimensional motion –What is the distance traveled in 3 seconds? –What is the acceleration at 1.25 hours? Speed, mph 321 0 0 10 20 Time, hours

59. Please Make friend with DVD experiments