Linear Motion

1. Linear Motion

2. Defining the important variables

3. Defining the important variables Kinematics is a way of describing the motion of objects without describing the causes. You can describe an object’s motion: In words Mathematically Pictorially Graphically No matter HOW we describe the motion, there are several KEY VARIABLES that we use.

4. Distance • Distance : How far something travels • It is a scalar quantity. It has magnitude but no direction

5. Displacement • Displacement: How far something travels in a given direction • It is a vector quantity because it has both magnitude and direction

6. SI Units • The SI Unit for distance and displacement is the meter. (m)

7. Speed Notes IV. Speed A.Speed is a quanitative measure of the rate of motion or a measure of how fast an object moves.

8. B.Speed is calculated by recording distance covered over a period of time: S = d t

9. t = dor d = St S

10. Velocity C.Velocity is speed in a given direction. Therefore: v = d t

11. Instantaneous Velocity D.Instantaneous Velocity – velocity at any given point.

12. Constant Velocity F.Constant Velocity - Maintaining velocity over a period of time.

13. Average Velocity G.Average Velocity – Average of velocities over a period of time.

14. Example #1 Ben watches a thunderstorm from his apartment window. He sees a flash of a lightening bolt and begins counting the seconds until he hears the clap of thunder 10.0s later. Assume that the speed of sound in air is 340.0 m/s How far away was the lightening bolt in a) in m? b) in km?

15. Example #2 On May 29,1988, Rick Mears won the Indianapolis 500 in 3.4h. What was his average speed during the 500 mi race? (Note: Generally the unit ‘miles’ is not used in Physics exercises. However, the Indianapolis 500 is a race that us measured in miles, so the mile is appropriate here. Don’t forget, the SI unit for distance is the meter.)

16. Example # 3 The slowest animal ever discovered was a crab found in the red Sea. It traveled with an average speed of 5.7 km/y. How long would it take this crab to travel 100 km?

17. Example #4 Tiffany, who is opening in a new broadway show, has some limo trouble in the city. With only 8 minutes until curtain call, she hails a cab and they speed off to the theatre down a 1000 m long one-way street at a speed of 25 m/s. At the end of the street the cab drives waits at a traffic light for 1.5 min. and then turns north onto a 1700 m long traffic filled avenue on which he is able to travel at a speed of only 10 m/s. Finally this brings them to the theatre.

18. Example #4 (con’t) • Does Tiffany arrive before the theatre lights dim? • Draw a distance time graph of the situation.

19. Graph Distance vs. Time 3000 2000 1000 Segment 1 Distance of 1000 m covered in short time, cab has high speed shown on a steep slope. Segment 2 Cab is at rest but time continues to pass Segment 3 Distance of 1700m covered in larger amt of time cab travels slowly. 0 100 200 300 Time (s) Slope is not steep.

20. Acceleration A.The rate at which velocity changes over the time interval during which it occurred.

21. B.Equation a = v = vf - vi t tf - ti • Greek Symbol meaning ‘change of’ Vf subscript

22. D.When acceleration increases its’ change is positive thus the acceleration is positive; when acceleration decreases its’ change produces a negative value.

23. E.Acceleration is the slope of a velocity - time graph slope = rise = v = a run t

24. F. Acceleration that does not change in time is uniform or constant acceleration. In this case, the velocity time graph is a straight line

25. H.Average acceleration is acceleration measured over a finite time interval.

26. G.Instantaneous acceleration is acceleration at a specific time; slope tangent to velocity time graph.

27. H.Average acceleration is acceleration measured over a finite time interval.

28. Example # 1 Grace is driving her sports car at 30 m/s when a ball rolls out into the street in front of her. Grace slams on her brakes and comes to a stop in 3 s. What was the acceleration of Grace’s car?

29. Kinematic #1 Example:A boat moves slowly out of a marina (so as to not leave a wake) with a speed of 1.50 m/s. As soon as it passes the breakwater, leaving the marina, it throttles up and accelerates at 2.40 m/s/s. a) How fast is the boat moving after accelerating for 5 seconds? 13.5 m/s

30. Kinematic #2 b) How far did the boat travel during that time? 37.5 m

31. Does all this make sense? 13.5 m/s 1.5 m/s Total displacement = 7.50 + 30 = 37.5 m = Total AREA under the line.

32. Interesting to Note A = HB Most of the time, xo=0, but if it is not don’t forget to ADD in the initial position of the object. A=1/2HB

33. Acceleration with distance

34. The displacement of an object in a given amount of time Δd = vo Δt + ½ a Δt2 If vo = 0 then Δd = ½ a Δt2

35. Kinematic #3 Example:You are driving through town at 12 m/s when suddenly a ball rolls out in front of your car. You apply the brakes and begin decelerating at 3.5 m/s/s. How far do you travel before coming to a complete stop? 20.57 m

36. Common Problems Students Have I don’t know which equation to choose!!!

37. Example # 1 Monica is walking to the hairdresser’s at 1.3m/s when she glances at her watch and realizes that she is going to be late for her appointment. She gradually quickens her pace at a rate of .09m/s2 • What is Monica’s speed after 10s? • B) At this speed, is Monica walking or jogging or running very fast?

38. Example #2 A torpedo fired from a submarine is propelled through the water with a speed of 20 m/s and explodes upon impact with a target 2000m away. If the sound of the impact is heard 101.4s after the torpedo was fired, what is the speed of sound in the water?