Physics Ch. 2, Motion in One Dimension

1. Physics Ch. 2, Motion in One Dimension

2. One dimensional motion: Something moves forward or backward.

4. *Reference point: A STATIONARY point from which to measure changes in position.

6. *Displacement The distance something travels from the point of reference. • Displacement = final position – initial position

8. A woodchuck starts at point 10 and ends at point 40, what is the displacement? • 30

9. Average Velocity: The displacement divided by the change in time. • (xf – xi / tf – ti) or delta x / delta t

10. After a 4 second play, Brett Favre gets sacked for a loss of 10 meters. What was his average velocity?

11. A squirrel had a velocity of 3 m/s for 9 seconds. How far did the squirrel travel?

12. Velocity is NOT the same as speed. • *For velocity, the DISPLACEMENT matters. For speed, only the distance matters. • Exp: A monkey climbs all the way up a 10 m tree and then down in 20 seconds, what is the vel? What is the speed?

13. If you graph position vs. time, the slope of the line at any point equals the velocity at that point. • Slope = Rise / Run • Slope = ∆X / ∆t

16. *Instantaneous Velocity The Velocity at one instant in time. • Find the instantaneous vel. by drawing a line that is tangent to the position vs. time graph, and find the slope of this line.

17. *Acceleration Describes how velocity changes over a time period.

19. Average Acceleration = Change in velocity / time • Aavg = ∆v/∆t = vf – vi / tf - ti

20. Usain Bolt goes from 4 m/s to 8 m/s in 2 seconds. What was his average acceleration? • 2 m/s2

21. Donald goes from 4 m/s to 2 m/s in 4 seconds. What was his avg. acceleration? • -.5 m/s2

22. Acc has direction and magnitude.

24. Constant Acceleration, vel. vs. time

25. Displacement depends on acceleration, initial velocity, and time. • Equations for constant acceleration situations: • ∆x = .5(vi + vf) ∆t

26. A runner accelerates from 0 m/s to 5 m/s in a time of 8 seconds. Find the distance traveled. • 20 m.

27. Vf = vi + a∆t • ∆x = Vi∆t + .5a(∆t)2

28. ∆x = Vi∆t + .5a(∆t)2 • A car travels 20 m in 5 seconds, with an acc. of 2 m/s2. What was the initial velocity? • -1 m/s

29. Vf2 = vi2 + 2a∆x

30. TABLE 4 has all these equations!

31. An aircraft has a landing speed of 83.9 m/s. The landing area is 195 m . What is the minimum uniform acc. needed for a safe landing? • Vf2 = vi2 + 2a∆x • -18 m/s2

32. Falling Objects • *Free Fall: The motion of an object when the only force acting on it is gravity.

34. *In free fall, acceleration is constant (-9.81 m/s2) in the downward direction.

35. How long would it take for a banana (.3 kg) to drop from the top of Mount Everest (8850 meters)?

36. If you throw a ball straight up with a velocity of 50 m/s, how long will it take to hit the ground? (multi-step problem)

37. Velocity vs. Time

38. PT Questions: Assume Constant acceleration • 1. A gorilla starts from running 1.5 m/s and runs 110 meters, eventually reaching a final velocity of 7 m/s. What was the gorilla’s constant acceleration? • 2. You are driving at 7 m/s. You then accelerate constantly for 14 seconds, traveling a total distance of 125 meters. What was your acceleration during this 14 second time period? • 3. Your friend Jake tells you he started driving 12 m/s, ended at 17 m/s, and his total trip lasted .3 hours. How far did Jake travel? • 4. A cheetah walks along at 1 m/s. Then, the cheetah gets chased by a grizzly bear, so it accelerates at 2 m/s2, eventually reaching a final velocity of 10 m/s. How far did the cheetah run during this acceleration?

39. Pipe-Cleaner Wheel Lab Need: Pipe-Cleaner, String, and Timers. Put this in your notebook. Questions on next slide. • Make a wheel out of a pipe-cleaner. • You will be rolling the pipe-cleaner on the ground from a set starting reference point. • Try to roll the pipe-cleaner on this path. For 5 rolls, take data on the distance, displacement, average speed, and average velocity. • Use string to trace out the distance path as well as you can, and measure it with a meterstick.

40. 1. Complete this table in your notebook: Write out all questions and your answers: • 2. Based on your experience with this lab, how is speed different from velocity? • 3. In a Nascar race, what would be a more useful stat for a driver to see after a race, avg. speed or avg. velocity? Why? • 4. Which trial gave you the best velocity? Describe the factors that went into producing a great velocity. • 5. Think of 3 situations where it would be more useful to know the total displacement rather than the total distance.

41. t = 0 t = 7 PRACTICE GRAPH

42. DRAWING ACTIVITY: • For the following position vs. time graph: • 1. Copy the graph from the next slide. • 2. Come up with a picture and a story that goes along with the graph. • 3. Explain how the motion changes during the key intervals: t= 0-2.9; 2.9-7.2; 7.2-9; 9-11; 11-12; 12-13; 13-14

43. t = 0 is here t = 7 t = 14

44. Interpreting Graphs Activity: • Go from station to station. Observe Graph, sketch it, and explain fully the motion it portrays. • They are hand-written out on Graph Paper (Mr. Hall drew the graphs)

45. Acceleration of a marble descending in corn syrup Lab • Make a hypothesis: Will the marble have +a or –a? WHY? • Fill a graduated cylinder to almost the very top with corn syrup. Then, SET the marble in. • You should have 2 timers. One should time from 100-50 ml and the other from 50-0 ml. • What was the velocity for the 1st half? 2nd half? What evidence is there that the marble accelerated/ decelerated? • How is the motion of the marble similar to an object in free fall? • What was your observation? Did it look as if the marble accelerated or decelerated? Explain.

46. Graph Drawing/ Vocab Partner Activity • Work with a partner and draw the following graphs or answer the following questions in your notebook.

47. Draw X vs. t graph, AND v vs. t graph for 1-3: • 1. A truck travels at a constant 5 m/s. Then it has a constant deceleration until it stops. • 2. A person rests for a while, decelerates for a brief period until reaching -2 m/s, then walks at a constant -2 m/s. • 3. A cheetah accelerates until it reaches 10 m/s. Then it runs at a constant 10 m/s. • 4. Why is there a negative sign in -9.81 m/s2? • 5. You start from rest and accelerate at .2 m/s2 until you reach the park. Then you turn around, and run back to where you started, this time accelerating at .15 m/s2. Will there be any identical velocities for your initial and return trip? Identical speeds? Explain.

48. 1. A truck travels at a constant 5 m/s. Then it has a constant deceleration until it stops.

49. 1. A truck travels at a constant 5 m/s. Then it has a constant deceleration until it stops.

50. 2. A person rests for a while, decelerates for a brief period until reaching -2 m/s, then walks at a constant -2 m/s.