1. Motion basics Chapter 1 Mr. Whitney

2. Sign Convention & Direction Motion has a 1) Direction 2) Magnitude - How much motion has or is occurring Positive: Up, to the right, North, to the East Negative: Down, to the left, South, to the West

3. Sign Convention & Direction Motion has a 1) Direction 2) Magnitude Needs a frame of reference, an origin to define positions at different times. Requires changes in TIME Uniform Motion means a time intervals are the same

4. Frame of Reference Coordinate systems Rectangular: x, y Polar: Radius (r), Angle ( )

5. Distance & Displacement Distance (x) equates Displacement equates to Difference between initial x i and final x f. x is position from the reference

6. Finding the angle Pythagorean theorem Sin(θ) = opposite/hypotenuse Cos(θ) = adjacent / hypotenuse Tan(θ) = opposite / adjacent 5/28/2016Physics6

7. Convert Coordinates Convert between Rectangular and Polar y = r  sin(θ ) y = opposite x = r  cos(θ ) x = adjacent y/x = tan(θ )r = hypotenuse

8. Kinematics Kinematics is the mathematical description of motion

9. Time and Displacement Displacement = change in position with direction x = x f – x i y = y f – y i Change in distance = final distance – initial distance (no direction, only magnitude) t = t f – t i Change in time= final time – initial time

10. Displacement Displacement is written:

11. A person moves on the number line shown below. The person begins at B, walks to C, and then turns around and walks to A. For this entire range of motion DETERMINE: a)the person’s final position b)the displacement c)the distance. Example 0 5 m 10 m 15 m A B C

12. Displacement verses Distance An RV travels 45 km east and stays the night at a KOA camp ground. The next day it travels for 3 hours to the north, traveling 110 km. What is the displacement over the two days for the RV? What is the distance over the 2 days for the RV?

13. Displacement verses Distance A delivery truck travels 18 blocks north, 10 blocks east, and 16 blocks south. What is the final displacement from the origin? (Assume the blocks are equal length) What is the distance the truck traveled?

14. Speed & Velocity Speed: How far Velocity: How Speed: distance traveled time interval Speed and Direction Velocity = x t

15. Average Speed & Velocity

16. Speed A trip to cape Canaveral, Florida takes 10 hours. The distance is 816 km. Calculate the average speed. How far (in meters) will you travel in 3 minutes running at a rate of 6 m/s?

17. EXAMPLE Usain Bolt holds the record for the 100m sprint completing it in only 9.58s! a ) Determine his average speed in m/s. (1.6km = 1mi) Did he run faster than this at some point?

18. Vectors Go Eastthen go West What is the final displacement? (this is a vector) What is the distance traveled? 5 mi3 mi

19. Vectors Go Eastthen go South What is the final displacement? (this is a vector) What is the distance traveled? 4 mi3 mi

20. Vector Notation Vector A  A A + B This adds the 2 vectors Vectors do not have to be in the same Direction to be added. See page 19 in textbook

21. Vectors and Trig Were A, B, and C are vectors (magnitude and direction) sin Θ = A/C cos Θ = B/C tan Θ = A/B

22. 1D Velocity HorizontalVertical

23. Compare to Slope Average Velocity v x avg =

24. Uniform Motion Be Careful !!! This equation only works for Uniform Motion (i.e. constant velocity) Good for when the initial position ≠ zero Alternate form: x f – x i = v x (t f – t i )

25. Position, Velocity, Acceleration

26. Component vectors All Vectors can be separated into x- vectors and y-vectors

27. Describing Motion: Kinematics in One Dimension

28. A commuter drives 15.0km on the highway at a speed of 25.0m/s, parks at work and walks 150m at a speed of 1.50m/s from his car to his office. Example b) Determine the average speed of the entire commute (a) Determine the total time of the commute.

29. Example: A woman starts at the entrance to a mall and walks inside for 185m north for 10minutes. She then walks 59m south in 3minutes to another store. She then leaves the store and moves south 155m in 8minutes to reach her car outside. Determine her average velocity during the trip.

30. Instantaneous Velocity The instantaneous speed or velocity is how fast an object is moving at a single point in time. Does the gauge on your dashboard give you speed or velocity? Does this gauge give you an average or instantaneous value?