Graphing Motion Part 2

Transcription

1 Kinematics 2: Motion Graphs & Free Fall Sep 5 10:34 AM Sep 5 1:25 PM Graphing Motion Part 2 How do you calculate the slope of a line? What would the slope of a distance vs time graph represent? What would the slope of a displacement vs time graph represent? What would the slope of a velocity vs time graph represent? You could memorize all of these, or you could just remember that slope= Sep 5 1:24 PM Sep 22 2:11 PM Position (or distance or displacement) vs time graph 1. During which intervals is the object stopped? 2. During which interval is the object s position changing the fastest? 3. What is the object s velocity during this time? Sep 23 9:12 AM Sep 22 2:15 PM

2 Velocity vs time graph 4. During which interval does the object have the highest velocity? 5. What is its velocity during this time? 6. What is the velocity from 8 9 s? Sep 22 2:15 PM Sep 4 8:12 PM Sep 23 9:12 AM Sep 23 9:12 AM Velocity (or speed) vs Time Graph 7. What is the acceleration from 0 4 seconds? 8. What is the displacement from 2 4 seconds? 9. What is the velocity from 9 10 seconds? 10. When is the velocity zero? Sep 23 9:13 AM Sep 22 2:16 PM

3 What does speeding up look like What does slowing down look like? Sep 22 2:17 PM Sep 7 3:03 PM Graphing Practice Sketch displacement vs time and velocity vs time for each 12. A man starts at a location 5 meters north of his house. He stands there for 3 seconds then walks away from his house with a constant speed of 1 meter per second. 11. A ball sits motionless on a table at a position 3 meters to the right of the origin. Sep 5 10:30 AM Sep 5 10:32 AM 13. A boy starts 6 meters west of his house. He runs toward his house with a constant speed of 10 meters per second and continues running by his house for 5 seconds then stops. 14. A woman leaves her house moving north at a constant velocity of 3 meters per second. After 5 seconds she gradually slows down until at 15 seconds she has stopped. Sep 5 10:32 AM Sep 5 10:32 AM

4 16. What is the acceleration of car A from 0 4 seconds? 15. Write a description for the following motion graph, and fill in the missing motion graph. 17. What distance does car A cover from 0 7 seconds? 18. What is the acceleration of car B from 0 7 seconds? 19. What is the acceleration for car B from 7 10 seconds? 20. What distance does car B travel from 4 7 seconds? 21. What is the velocity of car B at 5 seconds? 22. What is the displacement of car A over the entire 14 seconds? Sep 7 3:04 PM Sep 22 2:18 PM 23. The graph below represents the relationship between between line. Motion Graph Practice The most important thing to do with any motion graph is to read the axes. If you don t know what type of graph you re looking at, you will not know what to do to answer the questions involved. Slope from displacement > the first 4 seconds? 1. 5 m m m m DVA Slope from velocity > Area under velocity > Use the following graph for # What is the acceleration of the car at t=5.0 seconds? m/s m/s m/s m/s2 25. What is the total distance traveled by the car during this 6 second interval? m m m m Sep 22 2:19 PM 26. a. What type of graph is this? b. Sep 27 10:58 AM 27. a. What type of graph is this? What is the object doing from 2 5 seconds? b. What is the object doing from 0 3s? c. What is the displacement from 2 5 seconds? c. What is the velocity from 0 3s? d. What is the velocity at t=1 second? e. What is the acceleration from 2 5 seconds? d. What is the displacement from 0 3s? Sep 27 10:59 AM Sep 27 10:59 AM

5 28. a. What is the velocity at t=3 seconds? 29. a. What is the velocity at t=3 seconds? b. What is the acceleration from 4 6 seconds? b. What is the velocity at t=1 second? c. What is the displacement from 0 2 seconds? c. What is the velocity at t=5 seconds? d. What is the displacement over the entire 6 second e. What is the acceleration at t=1 second? d. What is the object doing from 4 6 seconds? Sep 27 10:59 AM Sep 27 10:59 AM 31. a. What is the object doing from 0 2 seconds? b. What is the object doing from 4 6 seconds? c. Calculate the acceleration of the object at t=2 s. 30. a. What is the speed of this object at t=3 seconds? d. Calculate the acceleration of the object at t=5 s. b. What is the displacement over the entire 6 seconds? e. Calculate the total displacement from 0 2 s c. What is the speed of this object from 4 6 seconds? b. What is the velocity of the object at t=2 s. Sep 27 11:00 AM Sep 27 11:00 AM What happens to an object as it falls? Oct 8 5:28 PM Oct 8 5:29 PM

6 'g' Acceleration due to gravity 'g' is different for different planets On Earth g = 9.81 m/s/s On the Moon g = 1.62 m/s/s On Jupiter g = 26 m/s/s Oct 8 5:29 PM Why do some objects seem to fall slower than others? What if objects were dropped in a vacuum? Oct 8 5:28 PM What happens when I drop an object? time 0 sec 1 sec Velocity Displacement Acceleration 2 sec 3 sec 4 sec Oct 8 5:29 PM When I drop an object, it starts: Oct 8 5:31 PM Oct 8 5:30 PM Position Velocity Acceleration Oct 8 5:31 PM

7 32. I drop a penny off the Empire State Building, which is 448.7m tall. How much time will it take until the penny hits an unsuspecting pedestrian? What is the initial velocity of the penny? What is the acceleration of the penny? What is the displacement of the penny (start to finish)? What is the question asking for? 36. The velocity time graph shows the velocity of an object dropped on the moon of Planet X. What is the acceleration due to gravity on this moon? 33. Mr. Vigneaux decides to jump out of an airplane from an altitude of 4000 m. How fast is he going when his parachute (hopefully) opens at an altitude of 1000 m? 34. An astronaut lands on Planet X and drops a marble from a height of 2 m. The marble hits the ground 3.2 seconds later. What is the acceleration due to gravity on Planet X, where the astronaut loses his marbles? 35. A helicopter drops a care package above a foreign country. The parachute on the care package is designed to open when the care package is traveling at 75 m/s. How much time will elapse between the care package dropping and the parachute opening? Sep 22 2:21 PM 37. a) Mr. Vigneaux drops an egg off the school building (11m tall) onto a student who failed the last exam, but he has bad aim and he misses. How long until the egg hits the ground? Sep 22 2:23 PM 40. A coin is tossed vertically upward (no air resistance). (a) Describe what happens to the velocity over the entire course of its path in the air (b) does the acceleration increase, decrease or remain constant while in the air? b) How fast is the egg moving when it hits the ground? When an object is dropped, what is the initial velocity of the object? 41. A pebble is dropped down a well and hits the water 1.25 sec later. Determine the distance from the top of the well to the water below. What if the object is thrown downward? What if the object is thrown upward? 38. A cat is thrown downward off a 125 m tall building with a speed of 10 m/s. a) What is the initial velocity of the cat? 42. A ball is thrown vertically upward, what are the velocity and acceleration at the peak where it reaches its maximum altitude. b) What is the acceleration of the cat? c) How fast is the cat going the instant it hits the ground? 39. A cannon fires a shot directly upward at 50 m/s. a) What is the initial velocity of the cannonball? 43. A cannon ball is launched directly upwards at an initial speed of 17.5 m/s. (a) What maximum height does it reach and (b) how long is it in the air for over its whole up and down trip. b) What is the acceleration of the cannonball? c) What is the speed of the cannonball at the instant it hits its highest point? (This question is important!!!) d) Create a motion graph that shows the ball going up and down. Circle the instant it hits the peak Displacement vs. Time Velocity vs. Time Accel vs. Time 44. A student throws a baseball vertically upward and then catches it. If vertically upward is considered to be the positive direction, which graph best represents the relationship between velocity and time for the baseball? [Neglect friction.] e) How much time does it take to reach this peak? f) How much total time does the cannonball spend in the air? Sep 22 2:24 PM Objects Launched Upwards A cannon fires a projectile directly upwards with an initial velocity of 40 m/s. 45. An insect jumps straight up into the air and you are able to record its maximum height of 0.8 meters before you scream and wave your arms in the air. Calculate the initial velocity of the insect the moment it jumps off the ground. Sep 27 11:03 AM 46. A jellyfish is launched out of the ocean with an initial velocity of 19.6 m/s. Two seconds later it reaches its maximum height. (a) How much total time does the jellyfish spend in the air? (b) With what speed will the jellyfish have when it returns to the ocean? Round g to 10 m/s to make the math easier. 2 Fill in the displacement (use d = vit + ½ a t ) for each position shown below 2 Fill in the velocity (use vf = vi + at) for each position shown below 47. An archer launches an arrow straight upward. (a) How fast does he have to shoot the arrow to hit a pigeon flying directly overhead at a height of 82 meters? (b) How much total time will the arrow spend in the air? Fill in the acceleration for each position shown below 48. A child shoots a spitball directly upwards. It hits goes straight up and then down and lands on his forehead 0.8 seconds later. What maximum height did the spitball reach? 49. Muggsy Bogues was 5 foot 3 inches tall (1.6 m) and could slam dunk a basketball. (a)how high did he have to be as high as the rim (3 meters above the ground)? (b) What initial velocity did he need to reach this height? (c) How much total time did he spend in the air? 50. Wile E Coyote accidentally catapults himself up with a speed of 46 m/s. (a) What maximum height does he reach? (b) What is his final velocity at the peak of his voyage? (c) How much total time does he spend in the air? (d) What is his final velocity when he returns to the ground? 51. A tauntaun on planet Hoth jumps upward with an initial velocity of 12 m/s. It returns to the ground 4.5 seconds later. (a) Calculate the acceleration due to gravity on planet Hoth. (b) What final velocity will the tauntaun have when it returns to the ground? (c) What maximum height will the tauntaun reach? Sep 27 11:04 AM Sep 27 11:04 AM

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