Motion in One Dimension

1. Motion in One Dimension AKA… Linear Motion

2. One-Dimensional Motion ______________ motion takes place only in one direction. Example: The train can move either forward or backward along the tracks. It cannot move left or right. In another words… An object can move _______ or ________, but not ____________ and _________ at the same time.

3. Frame of Reference ______________ – a system for specifying the precise location of objects in space and time “Another words, a reference point to measure _________________.” Example: ___________________

4. Distance • Is a _______ quantity • Has _________, but no _________ • Measures the _______ between two objects without indicating _______ from each other • Example: _____________________

5. Displacement • A _______ quantity • Has __________ and ___________ ____________ – change in position of an object Units: ___________ Displacement =

6. Example of Displacement • Displacement is _____ always equal to the distance traveled. Example if you walk three steps forward, and three steps back… Your distance is ???? Your magnitude is _______!

7. Displacement Continued • Displacement can be ______ or ______ • Unless otherwise stated, Displacement to the right is ______ Displacement to the left is ______ Upward displacement is _______ Downward displacement is _______ Examples: _______________________

8. Can be Pos or Neg…

9. 1. MOTION IS RELATIVE Everything moves, at least with respect to some reference point. To describe motion we shall talk about ___________ ___________ ___________

10. 2. Speed ___________ Speed is the speed you would read from a speedometer. = ___________ Units – _____________ Average Speed

11. 30 mph 2 miles ? Example of Average Speed B A • You take a trip from A to B and back to A. • You want to average 60 mph for the round trip A to B to A. From A to B you average 30 mph. What is your average speed on the return trip from B to A?

12. 30 mph 2 miles ? Example of Average Speed B A • 60 mi/hr is 60 mi/(60 min) or 1 mi/min. • To average 1 mi/min for a 4 mi trip would require 4 min. • 30 mi/hr is 30 mi/(60 min) or 1 mi/(2 min). • A 2 mi trip would take 4 min. • See a problem???

13. Speeding Little Old Lady Sorry, Ma’am, but you were doing 45 mph in a 30 mph zone. But I haven’t driven 45 miles yet. Okay, okay, would you believe that I haven’t been driving for an hour yet?

14. 3. Velocity • Average Velocity = ______________ • Units - _________________ • Instantaneous Velocity of an object is its _____________ plus the __________ it is traveling. • Velocity is a _________.

15. Speed vs. Velocity • Velocity is NOT the same as speed. • Speed has ________ only (how fast) Example: _______ • Velocity has _______ and _______ Example: ____________ **** +/- can serve as a direction

16. Average Velocity Units: meters per second, m/s Average Velocity = change in position change in time Vavg = Δ x = xf − xi Δ t tf − ti

17. Displacement and Average Velocity Distance traveled is the length of the path taken. Average velocity =

18. Velocity can be interpreted Graphically • When an object’s position is plotted versus time, the _____ of a position-time graph is the object’s velocity.

19. Instantaneous Velocity is NOT Average Velocity • Instantaneous Velocity is the velocity of an object at ________________ • Example: When you glance down at your speedometer while driving, the speed indicated by the speedometer is the magnitude of your instantaneous velocity. (or how fast you are going at that instant)

20. 4. Acceleration Acceleration = __________________ Units – Acceleration is also a ________. Has both magnitude and direction

21. Motion at constant velocity Accelerated motion Here Here, too

22. Demo - Ball on incline and ball on table • We can sense acceleration by comparing observations from a constant velocity frame of reference to observations from an accelerating frame of reference. • Interpretation - we can feel acceleration if there is a “support” force or contact.

23. Acceleration on Galileo's Inclined Planes

24. Velocity and Acceleration • Galileo used ____________ to study accelerations. • He found constant accelerations for inclines: the _______ the incline, the _______ the acceleration. (It was too hard to measure time for free-falls.) • He also found that the size of the objects ______ matter.

25. Average Acceleration Average Acceleration = aavg = Units: ________

26. Determining Acceleration Graphically • When a graph of an object’s velocity over time is produced, the slope of the _____________ graph is the acceleration of the object. • When the velocity of an object is constant, the acceleration is _____.

27. Velocity and Acceleration • An object with a + velocity and + acceleration is __________ • An object with a + velocity and - acceleration is __________ • An object with a - velocity and - acceleration is __________ • An object with a - velocity and + acceleration is __________

28. Negative Values • A negative value for the acceleration of an object does not always indicate that the object is decelerating. If the object is traveling in the negative direction, a negative acceleration would result in the object moving ________ in the _______ direction.

29. Relationships Between v and a for Linear Motion. If initial velocity is zero, then

30. Example A jogger starts at zero velocity with an acceleration of 3 ft/s2. How fast is she moving after 4 seconds? (Let’s see if we can first do this without using any equations.)

31. Chapter 3 Review Questions

32. What is the average speed of a horse that gallops a round-trip distance of 15 km in a time of 30 min? (a) 0 (b) 0.5 km/h (c) 30 km/h (d) 500 m/s (e) None of the above

33. What is the average velocity for the round-trip of the horse in the previous question? (a) 0 (b) 0.5 km/h (c) 30 km/h (d) 500 m/s (e) None of the above

34. Some formulas relating to displacement, velocity, and acceleration: • Finding Displacement with Constant Uniform Acceleration ∆x = ½ (Vi + Vf) ∆t • Finding Final Velocity with Constant Uniform Acceleration Vf = Vi + a∆t

35. Formulas Continued • Finding Displacement with Constant Uniform Acceleration ∆x = vi∆t + ½ a (∆t)2 • Finding Final Velocity after Displacement Vf2 = Vi2 + 2a∆x

36. 5. FREE FALL Motion near the surface of the earth in the absence of air resistance, ______ ___________________________. The acceleration of an object is g = __________ = _____________.

37. David Scott and the moon • David Scott demonstrated this on the moon in 1971 when he dropped a hammer and a feather at the same time. Both the hammer and the feather landed on the moon’s surface at _____________ time.

38. A Ball thrown upward: • While its velocity is positive (up), the acceleration on the ball is negative (down), so the ball ____________ as it climbs. • At the top of the balls flight, its velocity is reduced to zero, but its acceleration will still be _________ (downward). • As the ball falls, its velocity is ______ (down) and its acceleration is ______ (down), so the ball ____________.