verage speed and average velocity calculations

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INTRODUCTION TO MOTION

• The simplest idea in all of motion is: _________________________ • The most difficult idea in all of motion is: _________________________ • The most mysterious idea in all of motion (according to Lapp anyway) is: _________________________ What is a reference frame and why is it necessary when talking about motion? Motion Terms: • Distance: • Displacement: • Speed: • Velocity: Average speed and average velocity calculations: 1. A physics student leaves home, walks to school (4 blocks east) and then returns home for lunch. After lunch,

she returns to school. a. What is the distance of her journey? b. What is the displacement of her journey? 2. A skydiver, with parachute unopened, falls 625 m in 15.0 s. Then he opens his parachute and falls another 356

m in 142 s. What is his average speed for the entire fall? 3. A car drives according to the diagram to the right. Assume that there is a 1.0-hour

rest period after the first leg of the trip. a. Determine the average speed for the trip. b. Determine the average velocity for the trip.

Name (printed) _______________________________ First Day Stamp

40 mph for 0.50 h

30 mph for 0.50 h

60 mph for 0.25 h 60

mph

for 0

.25

h

2

Finish this page on your own with your partner and show me when you are finished. 1. A drug dealer travels 4.0 hours at 50 miles per hour east in order to sell some crack cocaine. He samples some

for himself and has to rest for an hour. Then he turns around, taking the same route halfway back to where he started. During the return trip, he only travels at 20 miles per hour west.

a. What is his average speed? b. What is his average velocity? 2. You maintain a speed of 115 mph for 2.0 hours. After resting for 45 minutes, you then return along the same

route to where you started. On the way back, you hold it down to 55 mph. What is your average speed for the entire trip?

STOP! IF YOU MOVE BEYOND THIS POINT WITHOUT GETTING CHECKED THERE WILL BE A PENALTY. Move ahead

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QUESTIONS AND PROBLEMS LINEAR MOTION

Go to the Physics Classroom website, physicsclassroom.com. In the section called Concept Builders choose Kinematics. Answer the questions in the following subsection until you acquire all three of its trophies. Show me the trophy collection or take a screen shot to get credit for completing the questions. Distance vs. Displacement 1. _____ An average speed of zero means: a. no motion b. possible motion c. definite motion 2. _____ An average velocity of zero means: a. no motion b. possible motion c. definite motion 3. _____ A distance of zero means: a. no movement b. possible movement c. definite movement 4. _____ A displacement of zero means: a. no movement b. possible movement c. definite movement

For the next four problems, show calculations in the space given. 5. _____ If you travel 50 miles east and then turn around and travel 80 miles west, what distance have you traveled? a. 30 miles b. 50 miles c. 80 miles d. 130 miles 6. _____ If you travel 50 miles east and then turn around and travel 80 miles west, what is the size of your

displacement? a. 30 miles b. 50 miles c. 80 miles d. 130 miles 7. _____ You travel at 60 MPH west for 40 minutes and then 30 MPH east for 20 minutes and then 40 MPH west

for 1.0 hour. What is your average speed? a. 29 MPH b. 35 MPH c. 43 MPH d. 45 MPH 8. _____ You travel at 60 MPH west for 40 minutes and then 30 MPH east for 20 minutes and then 40 MPH west

for 1.0 hour. What is your average velocity? a. 29 MPH b. 35 MPH c. 43 MPH d. 45 MPH 9. Shown to the right are the paths two motorcycles took on an

afternoon ride. Is the size of the displacement greater for Rider A, for Rider B or the same in both cases? Explain your reasoning.

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10. A physics teacher who lives 30 miles from school is frustrated by the low speed limit of 65 mph. He decides to go 80 mph instead. How many minutes of time does he save driving at the higher speed?

11. Your parents are those helicopter-like parents who want to control every event in your life and you’re trying to

prove to them that the college you want to go to isn’t that long a drive from home. You tell them to watch their clocks as you leave from home and head toward the college, telling them that you will call when you arrive. You speed off at 70 MPH for 100 miles, but then the weather turns bad and you slow it down to 50 MPH for the remainder of the trip. You make it from home to your college in 3.0 hours exactly.

a. How far is your college from home? b. What was your average speed for the trip? 12. A car drives for 1.5 hours at 60 mph east. Then the driver rests for an hour. Finally, the car drives for 3.0 hours

at 40 mph south. Determine the average speed for the trip. 13. One of the methods that the

Washington D.C. Police Department uses to catch speeders is to trigger multiple photographs of cars that pass through an automated radar zone at excessive speed. The photographs to the right were taken 0.20 s apart. The marker lines are five feet apart. The speed limit in this zone was 45 mph. By how much was this car exceeding the speed limit?


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LABETTE VECTOR FIELD TRIP

PURPOSE To learn how to add vectors and determine a resultant vector using graphical and analytic methods.

PROCEDURE 1. Learn to use a compass to find a bearing. • Point the “READ BEARING HERE” arrow in the direction you will move. • Rotate the compass wheel until the red half of the compass needle is in line with the North

arrow (see photo). • The bearing (or direction of movement) is the angle at the “READ BEARING HERE” line

(54.5° in photo). 2. Establish one partner as a walker, and count steps for walking the length between the two outer

poles that support the breezeway on the lawn side of the Boy’s Locker Room. Walk this length twice for accuracy. This distance has been carefully measured with a long tape measure, and it is 28.5 m. It will be used later to convert steps to meters.

3. From a starting position at the flagpole, walk in straight displacement vectors, being careful to take an accurate bearing and count your exact number of steps. You must walk toward the same breezeway pictured above and then continue through the breezeway and completely around Gus Gym until you reach the sign at the drop-off area that reads “PULL FORWARD FOR DROP-OFF.”

4. For every straight-line portion that you travel, be sure to record the number of steps taken and an accurate

measure of the bearing angle.

DATA AND ANALYSIS

1. Number of steps to walk the breezeway (pictured above) = ____________ 2. Calculate the distance each step represents (show work): 3. Scale the distance column so that the vectors can be drawn on page 7 of this module. A good scale might

be 5 meters = 1 centimeter. Convert your vector distance (m) to a scaled distance (cm)

# Bearing (degrees) Length (# of Steps) Distance (m) Scaled Distance (cm)

1

2

3

4

5

6

7

28.5 m

6

GRAPHICAL ANALYSIS 4. Create a scale drawing of your vector walk on the next page. All drawings must have the following: a. Show the proper axes for bearing angle. This means showing a north-south vertical axis and an east-west

horizontal axis somewhere on the page. b. Draw each vector to scale, and show each vector in order of the vector walk, using “head to tail” addition. c. Label each vector with magnitude in meters and direction in degrees. For example, something like this:

18.2 m, 167˚. d. Show a sample conversion of one of your displacement vectors - from steps to meters, and then meters to

scaled centimeters. e. Draw the resultant vector, from the tail of the first vector (where you started at the flagpole) to the head of the

last vector (where you ended at the Drop-off sign.) Make this resultant vector bolder, to show it is not just another displacement vector from the data.

f. Determine the magnitude and direction of your resultant vector. This will be measured with a ruler and

protractor. Be sure to scale the resultant back up to meters from centimeters.

ANALYTICAL ANALYSIS 5. Considering north/south to be along the y-axis and east/west to be along the x-axis, determine the “x” portion by

using 𝒙 = 𝒅𝒄𝒐𝒔𝜽 and the “y” portion by using 𝒚 = 𝒅𝒔𝒊𝒏𝜽. Show the calculations for the x and y values of the first distance below

# Bearing - θ (degrees) Distance - d (m) “x” portion, x (m) “y” portion, y (m)

1

2

3

4

5

6

7

Total = Total = 6. Find the sum of all your x and y values and record them at the bottom of the table columns. 7. In the space below, make a rough vector sum diagram of these two totals and then use the Pythagorean formula

to calculate the resultant vector. Then use an inverse trig function to calculate the bearing angle. Go to the Physics Classroom website, physicsclassroom.com. In the section called Concept Builders choose Vectors and Projectiles. Answer the questions in the following subsections until you acquire all three of its trophies. Show me the trophy collection or take a screen shot to get credit for completing the questions. Component Addition passed

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GRAPHICAL VECTOR ADDITION FOR LAB DISPLACEMENT VECTORS

Go to the Physics Classroom website, physicsclassroom.com. In the section called Concept Builders choose Vectors and Projectiles. Answer the questions in the following subsections until you acquire all three of its trophies. Show me the trophy collection or take a screen shot to get credit for completing the questions.

Head-to-Tail Vector Addition Vector Addition (the second one down on the page)

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PROBLEM SOLVING WITH ACCELERATED MOTION

Equations of Motion:

1. 𝑣!" =!!"!#$!!"!#$

2. 𝑎 = !!!!!!

3. 𝑑 = 𝑣!𝑡 +!!𝑎𝑡!

4. 𝑣!! = 𝑣!! + 2𝑎𝑑

• If the motion is accelerated, only

equations 2, 3, and 4 can be used.

• d, vi, vf, and a are vectors, so you must be careful to indicate signs correctly.

• Every accelerated motion problem must have three givens indicated at the beginning of the problem.

• Think of what you might have: t, d, vi, vf, a. Look for both explicit and implicit givens.

1. a. A car, moving at 22 m/s, accelerates at a rate of 3 m/s2 for 7 s. How far does it travel during that time? b. What speed has the car reached at the end of the 7 s? c. If the car slowed at a rate of 4 m/s2 for how far would it travel before it stopped?

Do the last two on your own and then show your solutions to me. 2. Do page 40, #26 (Giancoli) 3. Do page 43, #74 (Giancoli)


Given:

Given:

Given:

Given:

Given:

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QUESTIONS AND PROBLEMS LINEAR ACCELERATED MOTION

Go to the Physics Classroom website, physicsclassroom.com. In the section called Concept Builders choose Kinematics. Answer the questions in the following subsection until you acquire all three of its trophies. Show me the trophy collection or take a screen shot to get credit for completing the questions. Acceleration 1. _____ It is possible to have a changing velocity even if the speed is constant. a. true b. false 2. _____ It is possible to have a changing speed even if the velocity is constant. a. true b. false 3. _____ An object travels 8 meters in the first second of travel, 8 meters again during the next second of travel,

and 8 meters again during the third second. Its acceleration is a. 0 m/s2 b. 5 m/s2 c. 8 m/s2 d. 10 m/s2 e. more than 10 m/s2 4. _____ The following are series of speeds at the end of a 1 sec, 2 sec, 3 sec, and 4 sec interval. Which series

shows uniform acceleration? a. 2 m/s, 3 m/s, 5 m/s, 8 m/s c. 2 m/s, 4 m/s, 6 m/s, 8 m/s b. 2 m/s, 4 m/s, 16 m/s, 256 m/s d. 2 m/s, 8 m/s, 18 m/s, 32 m/s

For all problems, show all givens in the upper left part of the space given. No givens = no credit.

5. In getting ready to slam-dunk the ball, a basketball layer starts from rest and sprints to a speed of 6.0 m/s in

1.5 s. Assuming that the player accelerates uniformly, determine the distance that he runs. 6. A jetliner is landing with a speed of 69 m/s. Once the jet touches down, it has 750 m of runway in which to

reduce its speed to 6.1 m/s. What is the average acceleration of the plane during landing? 7. A truck, traveling at a velocity of 33 m/s, comes to a halt by decelerating at 11 m/s

2. How far does the truck

travel in the process of stopping? 8. The length of the barrel of a primitive blowgun is 1.2 m. Upon leaving the barrel, a dart has a speed of 14 m/s.

Assuming that the dart is uniformly accelerated, how long does it take for the dart to travel the length of the barrel?

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9. A soccer player runs at a constant speed of 2.6m/s. For the next 18 m, he speeds up with an acceleration of 0.45m/s

2. What is his speed at the end of the run?

10. In a 100-m race, a sprinter explodes out of the starting block with an acceleration of 3.2 m/s

2, which she

sustains for 3.0 s. Then, her acceleration drops to zero for the rest of the race. What is her total time for the race?

11. Talking on his cellphone while he’s driving, a guy doesn’t see a deer run out in the road in front of him. He’s

traveling at 33 m/s and once he sees the deer, he slams on the brakes and is able to decelerate at 15 m/s2. If the deer is 35 m away when he starts braking, does he hit the deer?

12. A crack cocaine dealer is getting on the freeway (starting from rest) and trying to get away from some thugs to

whom he sold bad dope. He initially accelerates at 4.9 m/s2 for 10 seconds ... until he sees a Highway Patrol. Then he maintains his speed for another 30 s. How far did he travel during the entire episode?


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Freefall Motion Problem Solving • The idea of freefalling has everything to do with _____________________________

• and very little (if anything) to do with _____________________________ • Something is freefalling if … • What is the motion like for something that is freefalling?

1. 2. 3. 4.

1. What is the initial velocity of a dart fired straight upward if it reaches a maximum altitude of 2.7 m? 2. How much time does it take until the dart is moving at 1.0 m/s downward? 3. Imagine that the floor disappeared as the dart was moving downward. What would be the dart velocity when it

is 4.0 m below the floor?

€

vav =dt

€

a =v f − vit

€

d = vit + 12 at

2

€

v f2 = vi

2 + 2ad

Given:

Given:

Given:

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LABETTE PHYSICS OF A PLASTIC TOY POPPER

INTRODUCTION Once you understand a bit about the physics of motion, you look at toys much differently. You begin to look at toys critically, in terms of how many principles of physics they illustrate. A toy store becomes even more provocative and exciting than when you were a kid. The balloon that you blow up and release before tying off the end is obeying Newton’s Third Law of Motion. The spinning top that seems to defy gravity is an example of a rotating body obeying the Law of Conservation of Angular Momentum. There used to be a toy store in Petaluma called Aunt Julie’s. It was owned by a man named Ken (that always seemed odd to me). Ken loved kids and he had a great toy store. A kid could walk into his store and, with just about any amount of money, find a toy. There were bins of toys with prices as low as five cents. One day I was in Aunt Julie’s and there was a bin of what looked like halves of small hollow, rubber balls (Figure 9.9a). They were called poppers.

They only cost nine cents each so I bought them all. To play with one, you simply turn it inside out and then put it on a flat surface. After a few moments it pops up in the air about a meter or so. For some reason, they’re very addictive. The seeming simplicity of the poppers is deceptive. They’re more complicated than you might think. There are actually two different accelerations that occur, one right after the other. Inverting the popper puts potential energy into it. As it restores itself to its original shape, the stored energy produces a force on the table and the popper very quickly accelerates from rest up to its takeoff speed from the table. That final speed for the first acceleration becomes the initial speed for the freefall acceleration that occurs next. Your job is to work backwards from the average maximum height of the popper to answer a number of questions about the motion of the popper, ultimately determining the time of the “pop.”

PURPOSE To gain experience using the equations of motion as they apply to an accelerating

object.

PROCEDURE Invert a toy popper onto the lab table (Figure 9.9b) and let it “pop” into the air

several times, measuring its maximum height with a ruler or rulers each time.

DATA

Maximum Height of Popper (m)

Average maximum height of popper: ___________

QUESTIONS/CALCULATIONS (SHOW ALL WORK) For all problems, show all three givens in the upper left part of the space given. No givens = no credit. 1. Calculate the initial speed of the popper.

(Check this with me before you move on.)

Figure 9.9a: Plastic Popper

Figure 9.9b: Inverted Popper

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2. Calculate how fast the popper is moving after 0.20 s. 3. Calculate the time it takes to reach its maximum height. 4. Calculate how far the popper has risen in 0.30 s. 5. Let’s say that as soon as the popper popped, the table and floor disappeared. Calculate how long it would take

the popper to reach a point 5.0 m below where it started. 6. If the inverted popper restores itself by pressing on the table through a distance of about 1.5 cm, calculate the

acceleration of the popper as it pushes against the table. 7. Calculate the time of the pop.


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QUESTIONS AND PROBLEMS LINEAR MOTION – FREEFALL

Go to the Physics Classroom website, physicsclassroom.com. In the section called Concept Builders choose Kinematics. Answer the questions in the following subsections until you acquire all trophies. Show me the trophy collection or take a screen shot to get credit for completing the questions. Freefall Up and Down 1. _____ A ball tossed vertically upward rises, reaches its highest point, and then falls back to its starting point.

During this time the acceleration of the ball is always a. in the direction of motion c. directed upward b. opposite its velocity d. directed downward 2. _____ At one instant an object in free fall is moving upward at 50 meters per second. One second later its speed

is about a. 55 m/s b. 45 m/s c. 40 m/s d. 35 m/s 3. _____ A rock is thrown straight upward at 30 m/s. Approximately how much later will it return to where it was

initially released? a. 3 s b. 6 s c. 10 s d. 30 s 4. _____ If you drop an object, it will accelerate at a rate of -9.8 m/s2. If you instead throw it downwards, its

acceleration (in the absence of air resistance) will be a. less than -9.8 m/s2 b. -9.8 m/s2 c. greater than -9.8 m/s2 5. _____ A bullet is dropped into a river from a very high bridge. At the same time, another bullet is fired from a

gun, straight down towards the water. Neglecting air resistance, the acceleration just before striking the water

a. is greater for the dropped bullet c. is the same for each bullet b. is greater for the fired bullet d. depends on how high they started 6. _____ Someone standing at the edge of a cliff throws one ball straight up and another ball straight down at the

same initial speed. Neglecting air resistance, the ball to hit the ground below the cliff with the greater speed will be

a. the one thrown upward b. the one thrown downward c. neither - they will both hit with the same speed

For all problems, show all givens in the upper left part of the space given. No givens = no credit. 7. A ball is thrown straight down and accelerated by gravity. After 2.0 seconds, it is moving at 35 m/s. At what

velocity was it originally thrown?

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8. A hotshot baseball pitcher throws a baseball vertically upward. 7.20 seconds later the ball has a downward velocity of 21.5 m/s. What was the velocity of the ball when the pitcher threw it?

9. A mean wife wants to collect on her husband’s life insurance policy so she invites him to the observation deck

on top of a 95-story building, 427 m high. She coaxes him to look over – way over – the edge. Then she accidentally … “bumps” him.

a. Ignoring air resistance, what is the velocity of the guy when he strikes the ground? b. How much time does he have to think about how rotten his wife is? 10. The school gets a new high-dive for the pool and the star diver gives it a try, springing upward with the initial

speed of 2.2 m/s from the board (4.0 m above the water). What is his velocity when he strikes the water? 11. Two girls with slingshots are on the top of a cliff scouting for birds. They see two, one straight up and one

straight down. One girl fires a pebble straight up with an initial speed of 15 m/s and the other fires a pebble straight down with an initial speed of 9.0 m/s. How far apart are the two pebbles after 0.50 s?

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