Kinematics A train accelerates from rest at a rate of 2 m/(s*s), for a time of 20 seconds. How much distance does the train cover?

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1 Physics R Date: 1. A cheetah goes from rest to 60 miles per hour (26.8 m/s) in 3 seconds. Calculate the acceleration of the cheetah. Kinematics Equations Kinematics 2 How to solve a Physics problem: 1. Read the question carefully; find out what the question is asking for 2. List the given quantities with units 3. Find & write down the equation 4. Perform substitution with units 5. Solve! Make sure your solution has units 2. A racecar is travelling at 50 m/s. It decelerates at a rate of 3 m/s 2 until it comes to a stop. How far does it take the car to stop? What is the question asking for? List the given quantities with units What equation relates the known quantities to what is being asked? Substitute with units and solve. Does the answer make sense? 3. A train accelerates from rest at a rate of 2 m/(s*s), for a time of 20 seconds. How much distance does the train cover? What is the question asking for? What are the known quantities? What equation relates the known quantities to what is being asked? What units should the answer have? Substitute and solve 1

2 Hints: Just because a question is asking for acceleration, doesn t mean you have to use a = Δv / t. You can use any equation that has a in it, such as Pay attention to units! What variable is: 25 m/s? 2 x 10 3 m? 12 seconds? Use v = d / t if and only if acceleration is zero/the object travels with constant velocity Instead use: Look for hidden given quantities! Starts from rest = Comes to rest = 4. A car is speeding at 45 m/s when the driver notices a sign and slows down to 25 m/s at a rate of -1.5 m/s 2. How far does the car travel while it is slowing down? What is the question asking for? What are the known quantities? What equation relates the known quantities to what is being asked? What SI units should the answer have? 5. A rocket car is travelling at 150 m/s. The drag chute is deployed, and slows the car at a constant 5 m/s*s. How far will the car travel before it comes to rest? What is the question asking for? What are the known quantities? What equation relates the known quantities to what is being asked? What SI units should the answer have? 6. A car starting from rest accelerates at a rate of 3.5 m/s*s. How much time does it take the car to cover a distance of 400 m? What is the question asking for? What are the known quantities? What equation relates the known quantities to what is being asked? What SI units should the answer have? 2

3 7. An object accelerates at a rate of 6 m/(s*s) West for 4 seconds, until it reaches a velocity of 4 m/s West. What was the object s initial velocity? Not on reference table: Average Velocity/Speed 8. A car accelerates from rest to 15 m/s over a distance of 50 meters. What is the average speed of the car? 9. A jogger running at 3.8 m/s accelerates to 6.3 m/s in 12 seconds. What is the average speed of the jogger? 10. Rocky the flying squirrel speeds up from m/s as he falls from a tree. What is the magnitude of his average velocity during his descent? Kinematics Practice 11. A physics teacher throws a bagel at a student. The bagel starts from rest and accelerates at a rate of 25 m/s 2 as the teacher moves his arm a distance of 0.4 meters. What is the final speed of the bagel on release? 12. An airplane accelerates from 125 m/s to 175 m/s at a rate of 4.5 m/s 2. Over how much time did this acceleration take place? 13. A car traveling 10 m/s accelerates uniformly at 6.1 m/s/s for 7.0 s. How far does the car move? 14. A traveling vacuum salesmen increases the speed of his vacuum-mobile from 21 to 27 m/s in 12 seconds. What is the average speed of his auto? 3

4 15. An airplane must reach a velocity of 81 m/s for takeoff. If the runway is 1.0 km long, what must the acceleration of the plane be? (Assume the plane starts from rest) 16. A car having an initial speed of 26 meters per second is uniformly brought to rest at a rate of 4.0 m/s/s. How far does the car travel during its deceleration? 17. Find the acceleration experienced by an object that changes velocity from 24 m/s to 96 m/s in an 8.0-second period. 18. Find the average speed of an object that changes velocity from 24 m/s to 96 m/s in an 8.0 second period. 19. In a race, a runner traveled 14 meters in 4.0 seconds as she accelerated uniformly from rest. What is the magnitude of the runner's acceleration? A little bit more challenging: 20. A car accelerates from rest to a speed of 15 m/s in 5 seconds. How far does it travel? 21. A car traveling on a straight road at 5.0 meters per second accelerates uniformly to a speed of 20.0 meters per second in 12.0 seconds. What is the total distance traveled by the car in this 12.0-second time interval? 22. A race car accelerates from rest at a rate of 8.7 m/s 2. How much time will it take to reach the end of an 1/4 mile race? (1 mile = 1609 m) 23. An ant is rushing along at a speed of 1.5 cm/s. He speeds up to 3 cm/s over a distance of 0.5 m. What is his acceleration in m/s 2? 4

5 Displacement (m) 24. A jet plane traveling at 120 m/s lands on a runway and slows down at a rate of -4 m/s 2. How long must the runway be for the plane to come to rest? 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= Position (or distance or displacement) vs time graph Position vs Time Time (s) 25. During which intervals is the object stopped? 26. During which interval is the object s position changing the fastest? 27. What is the object s velocity during this time? 5

6 Velocity (m/s) Displacement (m) 28. During which interval does the object have the highest velocity? 29. What is its velocity during this time? 30. What is the velocity from 8-9 s? Time (s) Velocity (or speed) vs Time Graph Slope Area 31. What is the acceleration from 0-4 seconds? What is the displacement from 2-4 seconds? What is the velocity from 9-10 seconds? 34. When is the velocity zero? Time (s) 6

7 Velocity (m/s) Car A solid, Car B dashed Time (s) 35. What is the acceleration of car A from 0-4 seconds? 36. What distance does car A cover from 0-7 seconds? 37. What is the acceleration of car B from 0-7 seconds? 38. What is the acceleration for car B from 7-10 seconds? 39. What distance does car B travel from 4-7 seconds? 40. What is the velocity of car B at 5 seconds? 41. What is the displacement of car A over the entire 14 seconds? 42. The graph below represents the relationship between speed and time for an object moving along a straight line. Use the following graph for #43-44 What is the total distance traveled by the object during the first 4 seconds? 1. 5 m m m m 43. What is the acceleration of the car at t=5.0 seconds? m/s m/s m/s m/s What is the total distance traveled by the car during this 6-second interval? m m m m 7

8 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 -> Slope from velocity -> DVA Area under velocity -> 45. a. What type of graph is this? b. What is the object doing from 2-5 seconds? c. What is the displacement from 2-5 seconds? d. What is the velocity at t=1 second? e. What is the acceleration from 2-5 seconds? 46. a. What type of graph is this? b. What is the object doing from 0-3s? c. What is the velocity from 0-3s? d. What is the displacement from 0-3s? 47. a. What is the velocity at t=3 seconds? b. What is the velocity at t=1 second? c. What is the velocity at t=5 seconds? d. What is the object doing from 4-6 seconds? 8

9 48. a. What is the velocity at t=3 seconds? b. What is the acceleration from 4-6 seconds? c. What is the displacement from 0-2 seconds? d. What is the displacement over the entire 6 seconds? e. What is the acceleration at t=1 second? 49. a. What is the speed of this object at t=3 seconds? b. What is the displacement over the entire 6 seconds? c. What is the speed of this object from 4-6 seconds? 50. 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. d. Calculate the acceleration of the object at t=5 s. e. Calculate the total displacement from 0-2 s f. What is the velocity of the object at t=2 s. 9

10 What happens to an object as it falls? Free-Fall g is different on different planets Earth Moon Jupiter Why do some objects fall slower than others? What if objects were dropped in a vacuum? What happens when I drop an object? Time (s) Velocity (m/s) Displacement (m) Acceleration (m/s 2 ) t = 0 t = 1 t = 2 t = 3 t = 4 When I drop an object, it starts: Motion graph for a dropped object in free fall Displacement vs. Time Velocity vs. Time Accel vs. Time 10

11 Velocity (m/s) (Ignore air resistance for all problems) 51. 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? 52. 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? 53. 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? 54. 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? 55. 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? Time (s) 11

12 56. 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? 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? What if the object is thrown downward? What if the object is thrown upward? 57. 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? b) What is the acceleration of the cat? c) How fast is the cat going the instant it hits the ground? 58. A cannon fires a shot directly upward at 50 m/s. a) What is the initial velocity of the cannonball? 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 e) How much time does it take to reach this peak? f) How much total time does the cannonball spend in the air? 12

13 59. 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? 60. 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. 61. A ball is thrown vertically upward, what are the velocity and acceleration at the peak where it reaches its maximum altitude. 62. 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. 63. 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.] 64. 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. 13

14 Objects Launched Upwards A cannon fires a projectile directly upwards with an initial velocity of 40 m/s. Round g to 10 m/s 2 to make the math easier. Fill in the displacement (use d = v i t + ½ a t 2 ) for each position shown below Fill in the velocity (use v f = v i + at) for each position shown below Fill in the acceleration for each position shown below Notice that free-fall is a mirror image up and down! Time up = time down, initial velocity at the ground = final velocity when it returns to the ground (but don t forget final velocity at the peak = 0) 14

15 65. 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? 66. 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? 67. 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? 68. 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? 69. 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? 70. 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? 15

16 Review Checklist Use equations to determine distance; displacement; speed; velocity; acceleration; or time. 1. How far does an object travel if it starts from rest and accelerates at a rate of 2.0 meters per second 2 for 6.5 seconds? 2. What is the final speed of a cart that begins with a velocity of +3.0 meters per second if it accelerates at a rate of +1.5 meters per second 2 while traveling +25 meters? 3. At what rate does an object accelerate if it changes its speed from 3.0 meters per second to 5.0 meters per second while traveling a distance of 4.0 meter? 4. How long does it take for an object to reach a velocity of 2.0 meters per second north if it begins with a velocity of 8.0 meters per second south and accelerates north at a rate of 4.0 meters per second 2? 5. A race car starting from rest accelerates uniformly at 4.9 m/s 2. What is the car s speed after it has traveled 120 meters? 6. A car initially traveling at a speed of 16 meters per second accelerates uniformly at a rate of 2.9 m/s 2 for 12 seconds. What distance does the car travel? 7. Jimmy accelerates his car from rest to 25 m/s over a distance of 100 meters. What is his average speed over this time? 8. A train slows from 30 m/s to 20 m/s in 4 seconds. What is the magnitude of the average velocity of the train during this time? Interpret graphs of distance or displacement vs. time. Calculate speed/velocity from a distance/displacement graph. Interpret graphs of speed or velocity vs. time. Calculate acceleration from a speed/velocity graph. Calculate distance/displacement from a speed/velocity graph. 9. When is this object moving fastest? What is its speed during this interval? 10. What is the speed of the object at t=8 s? 11. What is the speed of the object from 9-10 s? 12. During what intervals is the object not moving? 13. What is the speed of this object at t=3 seconds? 14. What is the speed of this object from 1-2 seconds? 15. When does the object have the highest speed? What is it? 16

17 16. When is this object not moving? 17. What is the speed of the object from 1-4 seconds? 18. How much distance does the object travel from 0-4 seconds? 19. What is the acceleration of this object from 0-2 seconds? 20. What is the acceleration of this object from 2-3 seconds? 21. What is the displacement from 0-4 seconds? 22. When is the object not moving? 23. What is the acceleration of the object from 3-4 seconds? 24. What is the acceleration of the object from 4-5 seconds? Explain the behavior of objects in free-fall (in the absence of air resistance.). Understand the terms dropped and maximum height. 25. What speed will a ball reach if it falls from rest for 3.0 seconds? 26. How far will a dropped object have fallen after 2.0 seconds? 27. What maximum height will an object reach if it thrown directly upward with a speed of 15 meters per second? How long will it take to reach this height? 28. What is the height of an object that is thrown upward with a speed of 20 meters per second 1.5 seconds after it is thrown? 29. An object is thrown directly upward with a speed of 25 meters per second. How long will it take to come back to the position from which it was released? 17

18 30. How long does it take for an object that is dropped from the top of a 45 meter high building to reach the ground? 31. An elephant drops a peanut, which hits the ground with a speed of 6 m/s. What is the average speed of the peanut on its trip to the ground? 32. A marble launcher shoots a marble directly upwards. The marble reaches a height of 1.8 meters. a. What is the initial velocity of the launched marble? b. What is the acceleration of the marble at the peak? c. The marble returns to the marble launcher. What speed does it have when it hits? 33. An angry bird shoots directly upwards from a slingshot with an initial velocity of 35 m/s. a. How much time does it take the bird to reach the peak? b. How much total time does the bird spend in the air? c. With what speed is the angry bird moving when it returns to the ground? The exam will be comprehensive. Go over the review checklist in Kinematics 1 and Physics Skills also. Answers to Review Checklist m m/s 3. 2 m/s s m/s m m/s m/s s, 3 m/s m/s m/s , 4-5, 6-9 s m/s m/s s, 5 m/s 16. 0s, 8-10s m/s m m/s/s m/s/s m 22. 0s, 4s, 8-10s m/s/s m/s/s m/s m m, 1.53 s m s s m/s 32. a. 5.9 m/s b m/s 2 c m/s 33. a. 3.6 s b. 7.2 s c. -35 m/s 18