Measurements & units Scalars & vectors Displacement, Velocity and acceleration Relative velocity.

1. CHAPTER 1 KINEMATICS • Measurements & units • Scalars & vectors • Displacement, Velocity and acceleration • Relative velocity. • Motion in two dimensions and in three dimensions • Special case: Gravity

2. Summary • Vectors: Positions, Displacement, Velocity and Acceleration.

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

4. Some Derivatives • Powers • Trig Functions • Exponentials

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

6. x (meters) 6 4 2 -2 t (seconds) 1 2 3 4 Instantaneous velocity What is the instantaneous velocity in the last second? • -2 m/s • 4 m/s • 1 m/s • 0 m/s

7. x (meters) 6 4 2 -2 t (seconds) 1 2 3 4 Average Speed What is the average speed over the first 4 seconds ? • 2 m/s • 4 m/s • 1,5 m/s • 0 m/s turning point

8. 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 ?

10. Part 4 Relative velocity.

11. Air speed Ground speed Brainstorming

14. Galilean formula of velocity sum

15. Learning Check

16. Solution a) Up

17. boat river ground Learning Check

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

20. Linear motion

23. Green car with solar cell 0 is certain point

24. Learning Check John is moving to x direction by equation: X= - 25t2 +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?

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

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

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

29. X=2+10t +4t2 (m) At t=3  x= 2+3.10 +4.9 = 68 (m) V= 10 + 8t (m/s) At x=4  4= 2+10t +4t2 4t2 +10t –2 =0  t = ? Learning Check

30. Part 5 Motion in two dimensions

31. Motion in two dimensions

32. Positions in 2 dimensions

34. Example • 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

35. Learning Check

37. Learning Check

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

42. History

47. Learning Check

48. 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.

49. 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

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