Name____________________________________________________Date__________Hour________

Physics EssentialsWorksheet Packet

Packet

Unit 2: Motion

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Comparing Distance and Displacement

Follow the directions below using a sheet of graph paper and a metric ruler. Then, answer the questions that follow.

Procedure1. Draw a dot at the intersection of two lines near the bottom edge of the sheet of

graph paper. Label the dot “Start”. 2. Draw a second, similar dot near the top of the paper. Label this dot “End”. 3. Draw a path from the Start dot to the End dot. Choose any path that stays on the

grid lines. 4. Use a ruler to determine the distance of your path. Write the distance below and

be sure to include units.

5. Use a ruler to determine the displacement from Start to End. Write the displacement below and be sure to include both units and the direction from Start to End.

Questions1. Which is shorter, the distance or the displacement?

2. How could you have made the distance shorter?

3. If you keep the Start and End points the same, is it possible to make the displacement shorter? Explain your answer.

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Unit 2: MotionChase’s Distance and Displacement

Directions: Read the following story and label each stop as a point on the graph paper that follows.

Chase had a busy day. He had to pick up his two best friends and take them to school with him. He first picked up Christian. Christian’s house is located 20 hectometers east and 18 hectometers south of Chase’s house. Next, he picked up Devon. Devon lives 26 hectometers south and 1 hectometer east of Chase. After school, which is located 4 hectometers north and 20 hectometers east of Chase’s house, they all went to rugby practice. The practice was on a field that is 11 hectometers west and 10 hectometers south of the school. After practice, Chase stopped by the ice cream store where his girlfriend Jasmine works. It is located 10 hectometers east and 14 hectometers south from the practice field. Jasmine wanted to introduce Christian to her friend Haley who works at the movie theater. It is located 5 hectometers east and 35 hectometers south of school. After they met Haley, Chase offered to drop Jasmine off at her house located 17 hectometers east and 5 hectometers south from Chase’s house.

1. Plot each “stop” Chase made as a dark dot and label it on the graph paper with the name.

2. Who should Chase have taken home first to travel the shortest possible distance? He can only drive on the “roads” which are the grid lines.

3. Calculate the shortest possible distance home from the movie theater (remember that he had to drop off three people). Show your calculations below:

4. Write out the directions you believe Chase followed home from above. Start at the movie theater and be sure to have 3 “stops” before reaching Chase’s house as the final stop. Use direction and number of decameters needed to reach each “stop”.

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5. Use a red colored pencil or pen to chart out the distance Chase traveled that day. Total distance traveled in red_________________(don’t forget units!!)

6. Use a blue colored pencil or pen to chart out an alternative route. Total distance traveled in blue_____________________(don’t forget units)

7. Use a highlighter and a ruler to trace Chase’s displacement to each “stop”. Add up all of the displacements _________________(don’t forget units)__.

8. Which number is greater, Chase’s total distance or the displacement from “stop” to “stop”? Why is that number greater?

9. THINK HARD!!!!! What was Chase’s TOTAL displacement that day? THINK!!!!!!!!!!!!!!!!!

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N 1 hectometer = 6 millimeters

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Speed Practice Problems

Answer the questions below using the formulas for speed and velocity as discussed in class. Be sure to show your work and include units with your answers.

Formula for determining speed:

Circle formula for speed:

Formula for determining velocity:

Practice problems – SHOW YOUR WORK!

1. In a boat race, Dan drove his motorboat over the 1000-meter course from start to finish in 40 seconds. What was Dan’s average speed during the race?

2. Different animal species show a tremendous range in their speed of movement. The fastest land animal, the cheetah, can travel 100 km/hr. In contrast, the slowest animal, a species of sea crab, has an average speed of just 5.7 km/yr. How long would it take the sea crab to travel 100.0 km?

3. You usually see lightening before you hear thunder, because light travels faster than sound. Juan saw a flash of lightening and heard the thunder 6 seconds later. Sound travels at a speed of 340 m/s in air. How far away was Juan from the lightening?

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4. In a competition, an athlete threw a flying disk 139 meters through the air. While in flight, the disk traveled at an average speed of 13.0 m/s. How long did the disk remain in flight?

5. If you shout into the Grand Canyon, your voice travels at the speed of sound (340 m/s) to the bottom of the canyon and back, and you hear an echo. How deep is the Grand Canyon in a spot where you can hear your echo 5.2 seconds after you shout?

6. Sound travels much faster in water than air. It takes 4.2 seconds for the sound of an explosion to travel underwater to a diver 6.006 m away. What is the speed of sound in water?

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Unit 2: MotionGraphing Speed by Making a Distance-Time Graph

Directions: Make a distance-time graph for a 3 hour car trip. The car covered 50 km in the first 30 minutes, stopped for 30 minutes, and

covered 100 km in the final 2 hours. Hints: Use as much of the graph area as possible. Note the three graph

segments!!

Questions and Conclusions:1. Which graph segment (between what times) slopes the most?

____________________________2. Which segment does not slope?________________________________________3. What was the car’s average speed in kilometers per minute? (show work below)

__________________________km/min4. What the car’s average speed in kilometers per hour? (show work below)

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5. What was the cars speed at 1.5 hours into the trip? _______________________(use units)

The following data were obtained for two runners:

6. Make a distance-time graph that shows the motion of both runners.

7. What is the average speed of each runner? Show work!

Sally____________ Alonzo___________

8. What is the instantaneous speed of each runner 1 second after he or she starts?

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Sally________________ Alonzo_______________

9. Which runner stops briefly? _________________________________10. During which interval do Sally and Alonzo run at the same speed? ____________________________The data below represent the Men’s World Records for May 2000.

11.Calculate the average speed in meters per second and in kilometers per hour for the 100 meter race. Show work!!!

_________________________m/s _______________________km/hr

12.Plot the data for 400 m to 10,000m on a distance-time graph on the graph paper on the next page.

13. What pattern do you notice in the graphed data?

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Unit 2: MotionVelocity Practice Problems

Write the formula for velocity and draw the circle diagram for velocity below.

Solve the following velocity problems. You must show all work and use Dimensional Analysis where appropriate in order to receive full credit.

1. What is the velocity (in m/s) of a spacecraft if it orbits the entire Earth, a distance of 27,000 miles, in only 1.5 hr? 1 mile = 1609 m

2. The Queen Elizabeth II takes 120 hours (5 days) to make a trans-Atlantic crossing to New York City, a distance of 3840 miles. What is her average velocity (in km/hr)?

3. How much time does it take a bullet to travel 100 m across a football field at 300 m/s?

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4. How long, in minutes, does it take light to travel from the Sun to the Earth? The distance is 150,000,000 km and the speed of light is 300,000 km/s.

5. It is a 60 mile bike trip around a lake. If you leave at 9 am and average 12 miles per hour, what time will you complete the trip?

6. A laser beam travels from the Earth to the moon and back in 2.667 s (round trip). The speed of light is 300,000 km/s. How far away is the moon?

7. If you walk around the Earth at the equator, about 25,000 miles at 3 mph, how long would the trip take you?

8. How many years would it take you to walk around the Earth if you walked for 8 hours per day?

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Graphing Practice Problems Velocity

Read each of the scenarios below. Draw the graph in the graph area provided to represent the information given in the scenario. Use a ruler or straightedge to draw straight lines.

1. Underdog can pursue a villain at the lightening quick speed of 5 m/s. Graph the distance he will cover if his chase lasts 5 seconds.

2. You were able to train your extremely brilliant dog, Einstein, to chase a Frisbee and catch it and then sit and wait for you to come over and get it from him. You throw the Frisbee a distance of 6 meters and it takes Einstein 4 seconds to run and catch it. Graph the distance Einstein will cover in 7 seconds.

3. Somehow you manage to get your hands on Flubber. To test how well it can bounce, you go out on the roof of your

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house, which is 12 meters high. It takes the Flubber 6 seconds to reach the ground, and then takes it 4 seconds to bounce back to a height of 10 meters. The Flubber then returns to the ground 2 seconds later and gets stuck in a large crack in the driveway. Graph the action of your Flubber.

For Questions 4-10, use the graph on the right to answer the questions. Write the correct answer in the space provided. Be sure to include the appropriate units.

4. How many meters can Swimmer 1 cover in 30 seconds?

5. How far will Swimmer 2 go in 30 seconds?

6. Predict the number of meters Swimmer 1 can go in 60 seconds.

7. Predict the number of meters Swimmer 2 can go in 60 seconds.

8. Which swimmer has the greatest speed?

9. Calculate the speed of Swimmer 1.

10. Calculate the speed of Swimmer 2.

11. Assume that both Swimmer 1 and Swimmer 2 swim at a constant speed. Given the speed that you calculated for Swimmer 1 and Swimmer 2, were your predictions for Questions 6 and 7 correct? Prove your answers using either the formula for speed or the slope method.

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18. An object moves at a slow, constant speed, then sits at rest for a moment, then moves at a new, faster, constant speed. Sketch a velocity-time graph of this motion on the axes below.

The position time graphs below represent different riders in a bicycle race. Match each graph with the description that makes the most sense and write the letter of the description next to the appropriate number. Some explanations will not be used.

A. slow, constant rate E. fast, constant rateB. started late F. gradually increasing speedC. went back to take a picture G. gradually decreasing speedD. spectator standing still H. leg cramp causes sudden drop in

speed

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_____19.

_____ 20.

_____ 21.

_____ 22.

_____ 23.

_____ 24.

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Use the information below to make a distance-time graph.

Robin, roller skating down a marked sidewalk, was observed to be at the following positions at the timeslisted below: Trial 1

Time (seconds) Position X (m)0.0 10.01.0 12.02.0 14.05.0 20.08.0 26.010.0 30.0

25. Plot the points on graph

26. How far was Robin from the original site 6 seconds after her start? ______________27. Was her speed constant over the entire interval? __________28. Please explain how you know the answer to #27.

Robin repeated her experiment. Her results from the second trial are listed below: Trial 2

Time (seconds) Position X (m)0.0 4.01.0 10.02.0 16.06.0 22.08.0 28.010.0 34.0

29. Plot the points on Graph

30. How far was Robin from the original site 5 seconds after her start? ______________31. How are her results from Trial 1 different from the results in Trial 2?

Unit 2: Motion

Acceleration Practice Problems

Write the formula for acceleration below.

Solve the following acceleration problems. You must show all work and use Dimensional Analysis where appropriate in order to receive full credit.

1. An astronaut is working outside the space station. Using her jet pack, she accelerates toward the entrance of the station. Her thrusters fire for 6 s and give her a velocity of 6 m/s. What is her acceleration?

2. A speed skater sprints toward the turn with an acceleration of 4.5 m/s2 and reaches the turn in 3 s. What is her change in velocity?

3. A car begins to slow down from 48 m/s as it approaches an intersection and stops at a red light. The car reaches the intersection in 12 s. What is the car’s acceleration?

4. A ball is dropped from a tall building. The acceleration due to gravity is 9.8 m/s2. If it takes 4 seconds to fall, how fast was it going just before it hit the ground?

5. How much time would it take a Corvette to go from 0 mph to 60 mph if it has an acceleration of 10 mph/s?

6. A wrecking ball suspended from a crane breaks loose and falls 30 m to the ground with a velocity of 30 m/s. How much time did it take to hit the ground?

7. An apple falls from a tree and hits Sir Isaac Newton in the head. If the apple had a velocity of 40 m/s and took 4 seconds to hit the old guy in the head, what was the apple’s acceleration?

8. Marvin the Martian is working outside of his space cruiser. He has dropped his wrench and is watching it slowly float away into outer space. In order to chase the wrench down, he fires the thrusters on his jet pack for 5 seconds, which gives him a velocity of 8 m/s. What is Marvin the Martian’s acceleration?

9. You are driving your dad’s new foreign convertible when you hear police sirens behind you. You look at your speedometer and see that you were traveling at 100 m/s. You can’t do the math fast enough in your head, but you realize you must have been speeding. You pull over on the side of the road and come to a complete stop as quickly as you can (it takes you 15 seconds). What is the acceleration?

10. A roller derby contestant is battling with her opponent to win the race. She sprints toward the turn with an acceleration of 4.5 m/s2 and reaches the turn in

3 seconds, knocking the other girl to the ground. What was her change in velocity?

11. You decide to get your Flubber out again. Instead of testing how high it can bounce, this time you want to look at its velocity before it hits the ground. You go back up on the roof of the house and throw it down to the driveway below. The acceleration due to gravity is about 10 m/s2 and it takes the Flubber 2.5 seconds to reach the ground. How fast was it going just before it hit?

Velocity(Speed)-Time GraphsDirections: Read through the information below then answer the questions that follow.

The first thing to note about velocity(speed)-time graphs is that, on first glance, they can look EXACTLY the same as Distance-Time graphs!

Spot the difference between these two graphs:

The only way you can tell the difference is by reading the labels on the x- and y-axes. ALWAYS read the labels on the axes – failure to do so can mean that you completely misinterpret what the graph shows!

Here are some basic speed-time graphs that you will need to learn:

A. CONSTANT VELOCITY (SPEED) This is a simple speed-time graph of a car trip. Don’t be tempted to think that the car was stationary! This is a speed-time graph, and the speed is both positive and constant. This graphs shows constant speed, which means that the car was not accelerating or decelerating.

B. POSTIVIE ACCELERATIONWhat about this one? What do you think it shows? If you guessed that it shows positive acceleration, you’re right! This speed-time graph represents a car that was accelerating down the road. The slope shows that the speed of the car was increasing every second.

c. NEGATIVE ACCELERATION This speed-time graph shows negative acceleration (or deceleration). The speed is decreasing, so the car must be decelerating, or slowing down. The slope of this graph shows that the speed was decreasing every second.

Problems: Using the information from above, answer the questions below:

1. What does this speed-time graph show you? Be specific!!

2. Speed-time graphs can be used to find out how far something has traveled. In this graph, a speed of 30 m/s is maintained for 20 seconds. How could you use this information to calculate distance?

20 40 60 80 Time (s)

8

6

4

2

Spe

ed (m

/s)

20 40 60 80 Time (s)

8

6

4

2

Spe

ed (m

/s)

Describe the car trips illustrated in the following graphs. Be sure to be very specific using units from the graph and describing each section:

Detailed Description#3

3.

4. Detailed Description#4

5. Detailed Description#5

The graph below shows how the speed of a bus changes during part of a journey.

20 40 60 80 Time (s)

8

6

4

2

Spe

ed (m

/s)

6. Describe the motion of the bus during each of the following segments:

O-A ___________________________________________________________________

A-B ___________________________________________________________________

B-C ___________________________________________________________________

C-D ___________________________________________________________________

D-E ___________________________________________________________________

E-F __________________________________________________________________

7. Now, use your graphing skills to plot the speed-time graph of the following car trip:

At the beginning, the car is traveling in a straight line at a constant speed of 3 m/s. After 20 seconds, the car accelerates up to a speed of 5 m/s, taking 15 seconds more to reach the new speed. After a total of 35 seconds, the car slows down, or decelerates. It takes the car an additional 20 seconds to decelerate from 5 m/s to 0 m/s. Thus, the total time for the car trip was 55 seconds.

Draw the velocity-time graph for an object

whose motion produced the distance-time

graph shown on the left.

8.

5 15 25 35 45 55 Time (s)

5

4 3 2

1

Spe

ed (m

/s)

9.

10.

Unit 2: MotionMotion Diagrams

Part 1 Dot Diagrams: Dot diagrams are very useful in showing the motion of an object. Each dot represents the position of the object at a constant time interval.

1. Describe, in words, the motion of the object depicted in the dot diagram below:

2. Draw the dot diagram of an object moving at a slow constant speed to the right.

3. Draw the dot diagram of an object moving at a fast constant speed to the right.

4. Draw a dot diagram of an object speeding up SLOWLY to the right (positive acceleration).

5. Draw a dot diagram of an object speeding up QUICKLY to the right (positive acceleration).

6. Draw a dot diagram of an object slowing down QUICKLY to the right (negative acceleration).

Analyze the following motion diagrams:Analyze the following motion diagrams:7. Below is the motion diagrams for two different objects A and B. Clock readings are indicated in the boxes.

a) Do both have uniform velocity? ___________b) Which is travelling fastest? ____________c) Which travels for the greatest length of time? ___________d) Which travels the greatest distance ? ___________e) At which clock readings(instants) do they occupy the same location at the same time? _____________________________________________________________________________________

8. Below is the motion diagrams for two different objects C and D. Clock readings are indicated in the boxes.

a) Do both have uniform velocity? ___________b) Which is travelling fastest to begin with? ______________c) Which travels for the greatest length of time? _______________________d) Which travels the greatest distance ? _____________________e) At which clock readings(instants) do they occupy the same location at the same time? ___________________________________________________________________________________f) Is there any time interval over which they have the same average velocity? ___________________________________________________________________________________g) Are they ever travelling the same speed at any clock reading? If so when? ___________________________________________________________________________________h) Describe the motion of C. __________________________________________________________ ____________________________________________________________________________________

g)Describe the motion of D. __________________________________________________________

___________________________________________________________________________________

Part 2 Vector Diagrams:To draw a vector diagram, you sketch 3 to 5 consecutive “frames” of the position of the object. Start by drawing the actual object at the initial position. Then, draw the object at the second position with an arrow representing the velocity at the next time interval. Repeat the drawing according to the velocity at each time interval. Remember that the size of the arrow should correspond to the magnitude of the velocity!!! Also recall that the greater the separation of the two objects, the faster the object is moving and vice versa.

9. Describe the motion of the car in the vector diagram below (include the term acceleration!!).

10. Describe the motion of the car in the vector diagram below (include the term acceleration!!).

11. Describe the motion of the car in the vector diagram below (include the term acceleration!!).

12.Construct a vector diagram of a car traveling toward the left at a constant speed.

13. Construct a vector diagram of a car traveling toward the left at a decreasing speed.

14. Construct a vector diagram for a bottle rocket whose burning fuel causes it to move vertically upward at an increasing speed.

15. Construct a motion diagram for the bottle rocket in #14 after its fuel burned and while it still moves upward but now at a decreasing speed>

7. Below is the motion diagrams for two different objects A and B. Clock readings are indicated in the

Unit 2: MotionVocabulary

Directions: Use your notes to define the following vocabulary terms. Use the following guidelines:

a. Words are to be hand-written on lined paper (no typed papers allowed).

b. Each word must be numbered as below.

c. You may use your completed vocab for the vocab quiz

1. Acceleration2. Average Speed3. Constant Acceleration4. Constant Speed5. Displacement6. Distance7. Distance-Time Graph8. Instantaneous Speed9. Kinematics10. Motion11. Motion Diagram12. Negative Acceleration13. Positive Acceleration14. Slope15. Speed16. Strobe Picture17. Ticker Tape Analysis18. Uniform Circular Motion19. Varying Speed20. Vector21. Vector Addition22. Vector Diagram23. Velocity24. Velocity-Time Graph