PHYSICS 211

CHAPTER 2 WORKBOOK

MOTION IN ONE DIMENSION

ANSWERS________________________________________________

STUDENT’S FULL NAME

________________________________________________DATE DUE

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PHYSICS 211 CHAPTER 2 MOTION IN ONE DIMENSIONCHAPTER OUTLINE

2.1 DISPLACEMENT

Define kinematics: The study of motion with regards to space and time only.

What is a frame of reference? A coordinate system with a starting point used to measure any quantity.

State the definition of displacement and write an equation for displacement. displacement is a change in position

What are vector and scalar quantities? a scalar is any physical quantity that can be represented by a single numerical

value.

A vector is any physical quantity that has a magnitude and a direction.

2.2 VELOCITY

Define average velocity and write an equation for average velocity. average velocity is the ratio of total displacement to the total time

How is the average velocity of a moving object interpreted from the object’s position vs timegraph?

average velocity between two points on a position vs time graph is the slope ofthe secant line between the two points

Explain what average speed is and how it differs from average velocity. How is average speedcomputed?

Average speed is the ration of total distance traveled to total time and it is apositive definite scalar. Average velocity is the ration of displacement to timeand is a vector.

avg speed =

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How is the instantaneous velocity of a moving object found from its position vs time graph?

inst vel at a point on a position vs time graph is the slope of the line tangent tothe graph at that point.

How is instantaneous speed related to instantaneous velocity?

inst speed is the magnitude of the inst velocity

2.3 ACCELERATION

Define average acceleration and explain how it is calculated. avg accel is the average change in velocity occurring over time.

Define instantaneous acceleration. inst is the rate of change of velocity, the limit as the time interval goes to zero of

the average acceleration

How are average and instantaneous acceleration interpreted from an object’s velocity vs timegraph?

avg accel is the slope of a secant line between two points on the graphinst accel is the slope of a tanget line at one point.

2.4 MOTION DIAGRAMS

What is a motion diagram?

a visual representation of an object’s motion at equal time intervals and showingvelocity and acceleration vectors.

If you are looking at a position vs time graph for an object’s motion, how would you identify asection that has a negative velocity and a positive acceleration?

the velocity is negative when the change in position is negative and theacceleration is positive when the position curve curves upward.

2.5 ONE-DIMENSIONAL MOTION WITH CONSTANT ACCELERATION

Paraphrase (in your own words) the 5 steps listed on page 36 for solving accelerated motionproblems:1. check for consistent units

2. set up a useful coordinate system and draw a motion diagram

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3. list the given data and the unknowns

4. consider relevant concepts and conditions then select a basic equation to calculateunknowns

5. check the answer for order of magnitude and units

2.6 FREELY FALLING OBJECTS

List the conditions for motion to be considered free-fall: no air resistance

acceleration is constant

What is the numeric value of the free-fall acceleration? Include units.

|a| = g = 9.8 m/s2

List the full set of free-fall equations when the positive y-axis is pointed upward:

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PHYSICS 211 CHAPTER 2 MOTION IN ONE DIMENSION MULTIPLE CHOICE QUESTIONS

Identify the letter of the choice that best completes the statement or answers the question.

B___ 1. A change in a physical quantity w having initial value wi and final value wf is given by which of

the following?a. wi - wf d. (wf - wi)/2 b. wf - wi e. none of the abovec. (wf + wi)/2

A___ 2. Displacement is which of the following types of quantities?a. vector c. magnitude b. scalar d. dimensional

A___ 3. Which of the following is not a vector quantity?

a. temperature d. displacement b. velocity e. force c. acceleration

A___ 4. In one-dimensional motion, the average speed of an object that moves from one place toanother and then back to its original place has which of the following properties?a. It is positive. d. It can be positive, negative, or zero.b. It is negative. e. It isn't zero. [THIS IS ALSO TRUE]c. It is zero.

D___ 5. In one-dimensional motion where the direction is indicated by a plus or minus sign, the averagevelocity of an object has which of the following properties?a. It is positive. d. It can be positive, negative, or zero. b. It is negative. e. It isn't zero.c. It is zero.

C___ 6. An object moves 20 m east in 30 s and then returns to its starting point taking an additional 50s. If west is chosen as the positive direction, what is the sign associated with the averagevelocity of the object?a. + d. any of the above b. - e. It isn't zero.c. 0 (no sign)

B___ 7. A bird, accelerating from rest at a constant rate, experiences a displacement of 28 m in 11 s.What is the average velocity?a. 1.7 m/s d. 4.2 m/s b. 2.5 m/s e. zero c. 3.4 m/s

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B___ 8. Jeff throws a ball straight up. For which situation is the vertical velocity zero?a. on the way up d. both a and c are correct b. at the top e. none of the abovec. on the way back down

C___ 9. Changing the positive direction in a reference frame to the opposite direction does not changethe sign of which of the following quantities?a. velocity d. displacement b. average velocity e. accelerationc. speed

B__ 10. On a position versus time graph, the slope of the straight line joining two points on the plottedcurve that are separated in time by the interval Dt, is which of the following quantities?a. average steepness d. average acceleration b. average velocity e. instantaneous acceleration c. instantaneous velocity

E__ 11. An x vs. t graph is drawn for a ball moving in one direction. The graph starts at the origin andat t = 5 s the velocity of the ball is zero. We can be positive that at t = 5 s,a. the slope of the curve is non-zero. d. the curve is at x = 0, t = 0. b. the ball has stopped. e. the slope of the curve is zero.c. the acceleration is constant.

B__ 12. A v vs. t graph is drawn for a ball moving in one direction. The graph starts at the origin and at t = 5 s the acceleration of the ball is zero. We know that at t = 5 s,a. the slope of the curve is non-zero. d. the curve is at v = 0, t = 0. b. the velocity of the ball is not changing. e. the velocity of the ball is zero. c. the curve is not crossing the time axis.

D__ 13. The value of an object's acceleration may be characterized in equivalent words by which of thefollowing?a. displacement d. rate of change of velocity b. rate of change of displacement e. the change of velocity c. velocity

C__ 14. In the case of constant acceleration, the average velocity equals the instantaneous velocity:a. at the beginning of the time interval. b. at the end of the time interval. c. half-way through the time interval. d. three-fourths of the way through the time interval. e. one-fourth of the way through the time interval.

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B__ 15. Two objects of different mass are released simultaneously from the top of a 20-m tower andfall to the ground. If air resistance is negligible, which statement best applies?a. The greater mass hits the ground first. b. Both objects hit the ground together. c. The smaller mass hits the ground first. d. No conclusion can be made with the information given.

B__ 16. A baseball catcher throws a ball vertically upward and catches it in the same spot when it

returns to his mitt. At what point in the ball's path does it experience zero velocity and non-zeroacceleration at the same time?a. midway on the way up b. at the top of its trajectory c. the instant it leaves the catcher's hand d. the instant before it arrives in the catcher's mitt e. midway on the way down

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PHYSICS 211 CHAPTER 2 MOTION IN ONE DIMENSIONADDITIONAL QUESTIONS

1. Calculate the overall average speed of a car that travels 100 miles in 3 hours followed by 150 miles in4 hours.

2. A runner averaging 8 m/s runs 5 km. How long does it take him?

3. A cat accelerates from rest at 1.5 m/s2. What will the cat’s speed be after 4.5 seconds?How far will it have traveled after 3 seconds?

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4. An airplane on the deck of an aircraft carrier must accelerate from rest to 175 mph in a distanceof 75 m. What average acceleration is required? How long does this take?

5. A car traveling 40 mph makes a smooth stop in 5.5 seconds. How far does it travel during thestop? What is its average acceleration?

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6. Electrons in an x-ray tube are accelerated from rest through a distance of 0.2 m in 1.5 ns. What isthe acceleration of the electrons? What is their final velocity?

7. A pebble is dropped from a bridge and splashes into the water 1.75 seconds later. How high isthe bridge above the water?

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8. A ball is thrown vertically upward from the ground at 12 m/s. To what maximum height does theball rise? How long is the ball in the air?

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PHYSICS 211 CHAPTER 2 MOTION IN ONE DIMENSIONEND OF CHAPTER PROBLEMS

Chapter 2 Practice Problems: 5, 6, 18, 22, 35, 39, 46, 51, 52, 57, 62, 67

Chapter 2 Homework Problems: 1, 11, 17, 21, 25, 29, 43, 49

1. A person travels by car from one city to another with different constant speeds between pairs of

cities. She drives for 30.0 min at 80.0 km/h, 12.0 min at 100 km/h, and 45.0 min at 40.0 km/hand spends 15.0 min eating lunch and buying gas. (a) Determine the average speed for the trip.(b) Determine the distance between the initial and final cities along the route.

11. A person takes a trip, driving with a constant speed of 89.5 km/h, except for a 22.0-min rest stop.If the person’s average speed is 77.8 km/h, how much time is spent on the trip and how far doesthe person travel?

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Figure P2.7

17. Find the instantaneous velocities of the tennisplayer of Figure P2.7 at (a) 0.50 s, (b) 2.0 s, (c)

3.0 s, and (d) 4.5s.

21. A certain car is capable of accelerating at a rate of +0.60 m/s2. How long does it take for this carto go from a speed of 55 mi/h to a speed of 60 mi/h?

25. In 1865, Jules Verne proposed sending men to the Moon by firing a space capsule from a 220-m-long cannon with final speed of 10.97 km/s. What would have been the unrealistically largeacceleration experienced by the space travelers during their launch? (A human can stand anacceleration of 15g for a short time.) Compare your answer with the free-fall acceleration, 9.80m/s2.

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29. A Cessna aircraft has a lift-off speed of 120 km/h. (a) What minimum constant acceleration doesthe aircraft require if it is to be airborne after a takeoff run of 240 m? (b) How long does it takethe aircraft to become airborne?

43. A ball is thrown vertically upward with a speed of 25.0 m/s. (a) How high does it rise? (b) Howlong does it take to reach its highest point? (c) How long does the ball take to hit the ground afterit reaches its highest point? (d) What is its velocity when it returns to the level from which itstarted?

49. A model rocket is launched straight upward with an initial speed of 50.0 m/s. It accelerates with aconstant upward acceleration of 2.00 m/s2 until its engines stop at an altitude of 150 m. (a) Whatis the maximum height reached by the rocket? (b) How long after lift-off does the rocket reach itsmaximum height? (c) How long is the rocket in the air? [HINTS: In part (a) you will need toknow the speed of the rocket when its engine quits. After its engine quits, its acceleration reverts

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to free-fall. Part (c) includes the time it takes the rocket to free-fall back to the ground.]