Unit 2 - Constant Velocity
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. The final position minus the initial position is the
a. average velocity.
c. time interval.
b. motion diagram.
d. displacement.
____
2. The speed is represented by
a. the ratio of the change of position to the time interval during the change.
b. the absolute value of the slope of a position-time graph.
c. the instantaneous velocity.
d. the time interval.
____
3. The magnitude of a vector represents its _____.
a. velocity
b. direction
c. size
d. color
____
4. Which choice is NOT a valid way to construct a motion diagram?
a. Add together the average speeds of the various objects in motion.
b. Take a series of photographs at equal time intervals of a moving object, perpendicular to
the direction of motion; overlay the images to see how the position changes with time.
c. Draw vectors to represent the velocities involved.
d. Add vectors in a head-to-tail manner to determine the resultant vector.
____
5. What is the result of two displacement vectors having opposite directions?
a. The resultant is the sum of the two displacements, having the same direction as the smaller
vector.
b. The resultant is the sum of the two displacements, having the same direction as the larger
vector.
c. The resultant is the difference of the two displacements, having the same direction as the
smaller vector.
d. The resultant is the difference of the two displacements, having the same direction as the
larger vector.
____
6. A factor that affects the behavior of a system is called a(n):
a. natural law.
b. experiment.
c. analysis.
d. variable.
____
7. The conversion factor for changing one unit of length to another in the metric system is a multiple of:
a. 3.
b. 10.
c. 12.
d. 5,280.
____
8. A racehorse is running with a uniform speed of 69 km/hr along a straightaway. What is the time it takes for
the horse to cover 400 meters?
a. 21 seconds
c. 0.35 hours
b. 2.1 minutes
d. 27.6 hours
____
9. A bird flutters around in a tree in a path described by the dark line:
Which vector represents the average velocity of the bird?
a.
c.
b.
d.
____ 10. If a drag racer wins the final round of her race by going an average speed of 198.37 miles per hour in 4.537
seconds, what distance did he cover?
a. 157,401 miles
b. 2.500 miles
c. 0.2500 miles
d. 0.0121 miles
____ 11. Duplain St. is 300 m long and runs from west to east between Baron and Burkey. If Keith is strolling east
from Baron at an average velocity of 3 km/hr, and Sue is power-walking west from Burkey at an average
velocity of 6 km/hr, how long will it take them to meet?
a. 1 minute
b. 2 minutes
c. 3 minutes
d. 6 minutes
____ 12. Assuming constant velocities, if a fastball pitch is thrown and travels at 40 m/s toward home plate, 18 m
away, and the head of the bat is simultaneously traveling toward the ball at 18.0 m/s, how much time elapses
before the bat hits the ball?
a. About 0.3 s
b. About 0.6 s
c. About 0.9 s
d. About 1.2 s
____ 13. A graph may be described as all of the following EXCEPT:
a. a tool to be interpreted ONLY by trained scientists and mathematicians.
b. used to describe the data collected from an experiment.
c. a picture showing how two variables are related.
d. easier to read than a table of numbers.
____ 14. Which of the lists show units arranged in order from smallest to largest?
a. Millimeter, centimeter, kilometer, meter
b. Centimeter, meter, kilometer, millimeter
c. Millimeter, centimeter, meter, kilometer
d. Meter, kilometer, millimeter, centimeter
____ 15. Which of the following lists of mass units are arranged in order from smallest to largest?
a. Gigagram, microgram, kilogram, megagram
b. Microgram, centigram, kilogram, gigagram
c. Milligram, microgram, centigram, kilogram
d. Megagram, kilogram, centigram, milligram
____ 16. How many seconds are in a stopwatch showing 1 hour, 3 minutes, and 5 seconds?
a. 68 seconds
c. 7,385 seconds
b. 245 seconds
d. 10,805 seconds
____ 17. The speed of a cheetah running 300 yards in 10 seconds is:
a. 30 yards per second.
c. 30,000 miles per hour.
b. 3,000 yards per minute.
d. None of the above
____ 18. Gwennen rides her bicycle 2.4 kilometers up a steep hill in 8 minutes. Her speed is ____ kilometers per
minute.
a. 0.3
b. 0.6
c. 3.3
d. 19
____ 19. Of the following, the largest unit of speed is:
a. meters per second.
b. kilometers per hour.
c. miles per hour.
d. inches per second.
Short Answer
20. What is the equation of motion for average velocity?
21. The position-time graph given below represents the motion of Ted returning home from the market on his
bike. What is the similarity between his displacement and the average velocity?
50
45
40
Position (m)
35
30
25
20
15
10
5
–1
–5
1
2
3
4
5
6
7
8
9
10
11
12
13
Time (s)
–10
22. Given below is the graph representing the position-time graphs of two swimmers (A and B), swimming in a
pool along a straight line. Both the swimmers start from two different positions. Use the graph to find when
and where swimmer B passes swimmer A.
350
Swimmer B
300
Position (m)
Swimmer A
250
200
150
100
50
–50
10
20
30
40
50
60
70
80
Time (s)
–100
23. A boy starts from point A and moves 5 units toward the east, then turns back and moves 3 units toward the
west. What is the displacement in the position of the boy?
24. What is the distance traveled by a vehicle in 12 minutes, if its speed is 35 km/h?
25. A bowler rolls a bowling ball down the gutter. The ball travels 60 feet in 5 seconds. Draw a particle model
motion diagram with 1 second intervals. Construct the corresponding position-time graph.
Below is a motion diagram for an inline skater going in a straight line. The time interval between successive
positions is 2 s.
26. What is the displacement of the skater after 8 s?
Essay
27. A boy is cycling at a constant speed along a straight road to his school. The positions of the boy after fixed
time intervals are observed.
a. What type of position-time graph can be expected for the motion of the bicycle?
b. How can the average velocity of the bicycle be calculated?
c. How is the average speed of the bicycle related to its average velocity?
28. Tom drives his car at a constant speed on a straight road for two hours while going to meet his friend. He
noted the position of his car after every 15 minutes, assuming his house to be the origin. On his way back
home, he again noted the positions of the car after every 15 minutes, without changing the origin. If on both
of the trips, his car covers 25 km in every 15 minutes, then:
a. Draw the position-time graphs of the car for the two sides of the journey.
b. Find the difference between the average velocities of the two sides of the journey.
c. Find what happens if during the return journey, the friend’s house is taken as the origin.
Unit 2 - Constant Velocity
Answer Section
MULTIPLE CHOICE
1. ANS: D
Displacement is the vector difference between initial and final positions.
PTS: 1
DIF: Bloom's Level 1|DOK 1
REF: p. 36
NAT: B.4
2. ANS: B
Speed is the absolute value of velocity, which is the slope of a position-time graph.
PTS: 1
DIF: Bloom's Level 1|DOK 1
NAT: B.4
3. ANS: C
A vector’s magnitude represents the vector’s size.
REF: p. 44
PTS: 1
DIF: Bloom's Level 1|DOK 1
REF: p. 35
NAT: B.4
4. ANS: A
A motion diagram is a series of overlapping snapshots, showing the motion of one or more objects.
PTS: 1
DIF: Bloom's Level 2|DOK 1
REF: pp. 32-33
NAT: B.4
5. ANS: D
When two displacement vectors have opposite directions, their resultant has a magnitude equal to the
difference between their magnitudes. The direction of the resultant is the same as the direction of the larger
original vector.
PTS: 1
DIF: Bloom's Level 3|DOK 2
NAT: B.4
6. ANS: D
PTS: 1
DIF: basic
STA: SC.H.1.4 | SC.H.2.4.1
7. ANS: B
PTS: 1
DIF: basic
STA: MA.B.2.4
8. ANS: A
(400 m)(1 km/1000 m) = 0.4 km
REF: p. 35
REF: section 1.1
REF: section 1.2
(0.4 km)(1 hr/69 km)(60 min/1 hr)(60 s/1 min) = 20.86 s = 21 s
PTS: 1
DIF: Bloom's Level 4|DOK 3
REF: p. 44
NAT: B.4
9. ANS: A
Choice A represents the head-to-tail sum of the vectors of the bird’s motion.
PTS: 1
NAT: B.4
DIF: Bloom's Level 3|DOK 1
REF: p. 35
10. ANS: C
4.537 seconds/60sec per min = 0 .07562 min
0 .07562 min/60 min per hr = 0.001260 hr
(198.37 mph)(0.001260 hr) = 0.2500 miles
PTS: 1
DIF: Bloom's Level 3|DOK 1
REF: p. 44
NAT: B.4
11. ANS: B
Sue is walking west at 6 km/hr = 6000m/60min = 100m/min.
Keith is walking east at 3 km/hr = 3000m/60 min = 50m/min.
By constructing a position-time graph for the two walkers, it can be seen that they will intersect after 2
minutes (Sue will have traveled 200 m, and Keith will have traveled 100 m.)
(Keith is dashed, Sue is solid.)
PTS: 1
DIF: Bloom's Level 3|DOK 2
REF: pp. 38-40, 43
NAT: B.4
12. ANS: A
Assume that the bat and ball are traveling on the same line, but in opposite directions. Draw the position-time
graph for each and read the time from where the lines cross:
13.
14.
15.
16.
17.
18.
19.
PTS: 1
DIF: Bloom's Level 4|DOK 3
REF: pp. 38-40, 43
NAT: B.4
ANS: A
PTS: 1
DIF: basic
REF: section 1.2
STA: SC.H.1.4 | MA.D.1.4.1 | MA.D.2.4.1
ANS: C
PTS: 1
DIF: intermediate REF: section 1.2
STA: MA.B.2.4
ANS: B
PTS: 1
DIF: intermediate REF: section 1.2
STA: MA.B.2.4
ANS: C
PTS: 1
DIF: intermediate REF: section 1.2
STA: MA.B.2.4
ANS: A
PTS: 1
DIF: intermediate REF: section 1.3
STA: SC.C.1.4 | MA.B.2.4.2
ANS: A
PTS: 1
DIF: intermediate REF: section 1.3
STA: SC.C.1.4 | MA.B.2.4.2
ANS: A
1 meter per second = 2.24 miles per hour , 3.60 kilometers per hour, 39.4 inches per second
These values may be calculated by the student using conversion factors discussed in class
e.g. 1 hour = 3600 seconds, 1 mile = 1.61 kilometers, 1 meter = 39.4 inches
PTS: 1
DIF: advanced
REF: section 1.3
STA: SC.C.1.4 | MA.B.2.4.2
SHORT ANSWER
20. ANS:
The equation of motion for average velocity is
. In this equation, d is the position of an object, is
the average velocity of the object, t is the time and di is the initial position of the object. According to this
equation, an object’s position is equal to the average velocity multiplied by time plus the initial position.
PTS: 1
DIF: Bloom's Level 1|DOK 3
REF: p. 47
OBJ: 2.4.3 Create pictorial, physical, and mathematical models of motion problems.
NAT: UCP.2 | B.4 TOP: Create pictorial, physical, and mathematical models of motion problems.
KEY: Average velocity
MSC: 2
21. ANS:
In this case, motion is in the negative direction. Therefore, displacement and velocity of the bike are negative.
Hence, both the displacement and the velocity have a negative sign.
PTS: 1
DIF: Bloom's Level 1|DOK 3
REF: p. 44
OBJ: 2.4.1 Define velocity.
NAT: B.4
TOP: Define velocity.
KEY: Displacement| Average velocity
MSC: 1
22. ANS:
The point of intersection of the two graphs is 150 m at about 38 s. Swimmer B passes Swimmer A about 150
m beyond the origin 38 s after A has passed the origin.
PTS:
OBJ:
TOP:
MSC:
23. ANS:
1
DIF: Bloom's Level 2|DOK 3
REF: p. 38
2.2.4 Determine a time interval.
NAT: B.4
STA: SC.C.1.4.1
Determine a time interval.
KEY: Time interval| Origin
2
The resultant displacement is 2 units toward the east, and his position is at 2.
PTS: 1
DIF: Bloom's Level 2|DOK 3
REF: p. 34
OBJ: 2.2.5 Use a motion diagram to answer questions about an object's position or displacement.
NAT: B.4
STA: SC.C.1.4.1
TOP: Use a motion diagram to answer questions about an object's position or displacement.
KEY: Displacement
MSC: 2
24. ANS:
Speed is given in km/h, therefore convert time in minutes to hours.
distance traveled = (speed)(time taken) = (35 km/h)(12 min)(1 h/60 min) = 7.0 km
PTS: 1
DIF: Bloom's Level 2|DOK 3
OBJ: 2.2.3 Define displacement.
NAT: B.4
KEY: Distance
MSC: 2
25. ANS:
REF: p. 36
TOP: Define displacement.
PTS: 1
DIF: Bloom's Level 5|DOK 3
NAT: B.4
26. ANS:
The displacement of the skater after 8 s is 48 m.
REF: pp. 33, 38
PTS: 1
NAT: B.4
DIF: Bloom's Level 4|DOK 3
REF: pp. 32-33, 36
ESSAY
27. ANS:
a. The bicycle is moving with a constant speed, and motion is in the straight line, without any change in
direction. The velocity of the bicycle is also constant. Therefore, the position-time graph will be a straight
line.
b. The average velocity of the bicycle is calculated as the slope of the position-time graph.
c. The average speed of the bicycle is the absolute value of its average velocity.
PTS:
OBJ:
TOP:
MSC:
28. ANS:
a.
1
DIF: Bloom's Level 3|DOK 2
2.4.2 Differentiate between speed and velocity.
Differentiate between speed and velocity.
2
REF: p. 44
NAT: B.4
KEY: Average speed| Average velocity
b. There is the difference of sign in the two velocities. During the return journey, the displacement is
negative. Therefore, the average velocity is also negative.
c. The average velocity during the return journey also becomes positive.
PTS:
OBJ:
TOP:
KEY:
1
DIF: Bloom's Level 3|DOK 3
2.3.1 Develop position-time graphs for moving objects.
Develop position-time graphs for moving objects.
Displacement| Position-time graph| Average velocity
REF: p. 38
NAT: B.4
MSC: 2