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

CHAPTER 1 KINEMATICS. Measurements & units Scalars & vectors Displacement, Velocity and acceleration Relative velocity. Motion in two dimensions and in three dimensions Special case: Gravity. Summary. Vectors: Positions, Displacement, Velocity and Acceleration. Vector or Scalar?.

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

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  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 ?

  9. Part 4 Relative velocity.

  10. Air speed Ground speed Brainstorming

  11. Galilean formula of velocity sum

  12. Learning Check

  13. Solution a) Up

  14. boat river ground Learning Check

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

  16. Linear motion

  17. Green car with solar cell 0 is certain point

  18. 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?

  19. 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

  20. 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.

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

  22. 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

  23. Part 5 Motion in two dimensions

  24. Motion in two dimensions

  25. Positions in 2 dimensions

  26. 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

  27. Learning Check

  28. Learning Check

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

  30. History

  31. Learning Check

  32. 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.

  33. 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

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

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