1111
True/False
Indicate whether the statement is true or false.
____
1. In a chosen coordinate system, the position of an object in motion can have negative values.
____
2. The slope of a position-time graph of an object gives the speed of the object.
____
3. A time interval is a scalar quantity.
____
4. The position-time graph of an object moving with a constant average velocity is always a straight line.
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
5. 1 micrometer (1 µm) equals:
a. 10–3 m
b. 10–6 m
c. 103 m
d. 106 m
____
6. What is the volume of a cube whose side is 10 cm?
a. 10–3 m3
c. 102 m3
3
b. 10 m
d. 103 m3
____
7. What is the number of significant digits in the measurement 34.000 m?
a. 2
c. 4
b. 3
d. 5
____
8. According to Boyles’ law, PV = constant. If a graph is plotted with the pressure P against the volume V, the
graph would be a(n):
a. straight line
c. hyperbola
b. parabola
d. ellipse
____
9. The time period T of a simple pendulum is given by the relation
, where L is the length of the
pendulum and g is the acceleration due to gravity at the place. From the above relation, we can say that:
a. T  g
c. T2  g
b. T  L
d. T2  L
____ 10. The slope of the graph given below is:
a.
b.
c.
d.
____ 11. A car is moving with a uniform speed of 15.0 m/s along a straight path. What is the distance covered by the car
in 12.0 minutes?
a. 1.02  0–3 km
c. 8.00  0–5 km
–1
b. 1.80  0 km
d. 1.08  01 km
____ 12. Which of the following is a pair of vector quantities?
a. Speed — Distance
c. Velocity — Displacement
b. Velocity — Distance
d. Speed — Displacement
____ 13. What is the resultant of two displacement vectors having the same direction?
a. The resultant is the sum of the two displacements having the same direction as the original
vectors.
b. The resultant is the difference of the two displacements having the same direction as the
original vectors.
c. The resultant is the sum of the two displacements having the direction opposite to the
direction of the original vectors.
d. The resultant is the sum of the two displacements having the direction perpendicular to the
direction of the original vectors.
Completion
Complete each statement.
14. The method of treating the units as algebraic quantities that can be canceled is called ____________________
analysis.
15. The valid digits in a measurement are called ____________________.
16. When the graph of best fit is a straight line, the dependent and independent variables have a(n)
____________________ relationship.
17. On a graph, the ____________________ is the ratio of the vertical change to the horizontal change.
18. The acceleration of the body in the graph given below is ____________________.
19. A(n) ____________________ model is a simplified version of a motion diagram that represents the object in
motion by a series of single points.
20. The vector that represents the sum of the other two vectors is called the ____________________.
Short Answer
21. The speed of a body is the distance traveled per unit time.
a. What is the SI unit of speed?
b. Is the unit of speed a basic unit or a derived unit?
22. What is the difference between 5.0 and 5.00?
23. The mass of a body measured by two persons is 10.2 kg and 10.23 kg. Which is more precise and why?
24. What can you say about the motion of a body if:
a. Its displacement-time graph is a straight line inclined with the time axis.
b. Its velocity-time graph is a straight line inclined with the time axis.
c. Its velocity-time graph is a parabola.
25. What conclusions can be drawn if a velocity-time graph is parallel to the time axis?
26. What conclusions can be drawn if a velocity-time graph is a curve?
27. The force acting on an object moving with constant acceleration is given by F = ma, where m is the mass of the
object measured in kg, a is the acceleration in m/s2, and F is the force acting on the object, measured in newtons.
What is 1 N described in base units?
28. The volume of a cuboid is the product of its length, breadth, and height. Give a possible metric unit for the
volume. Is the unit for volume a basic unit or a derived unit?
29. What conversion factor is used to convert 10 hours to seconds?
30. Two objects have masses m1 and m2 and their centers are separated by a distance d. The force of gravitation
between these objects is given by the expression
.
Here G is the gravitational constant. Find the units of measurement of G.
31. Write the number 13900 using scientific notation. What is the number of significant digits in this number?
32. What is two-point calibration?
33. The position-time graphs of two runners, Ian and Nick, are shown below. How can the faster runner be
determined using these graphs?
10
d
9
8
Ian
Position (m)
7
6
Nick
5
4
3
2
1
1
2
3
4
5
6
7
8
9
t
Time (s)
34. What is the type of speed-time graph of an object moving with a constant speed along a straight line? Name two
physical quantities whose values can be calculated using this graph.
35. What is a motion diagram?
36. What is the significance of defining a coordinate system to study the motion of an object?
37. How is displacement different from distance? Under what conditions can an object travel a certain distance and
yet its resultant displacement be zero?
38. What is the equation of motion for average velocity?
39. Define average velocity.
40. The position-time graph of an object is found to be a straight line passing through the origin. What information
about the motion of the object is provided by the graph?
41. Given below is the position-time graph representing motions of two runners, Nick and Ian. Use this graph to
determine which runner has greater average velocity.
10
9
8
Ian
Position (m)
7
6
Nick
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
Time (s)
42. Given below is the particle model of a boy skating on a smooth, pedestrian-free sidewalk. The time interval
between successive dots is 2 s.
Plot a position-time graph to represent the motion of the boy.
43. 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
Position (m)
40
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
44. Given below is the motion diagram of a small ball rolling straight on a frictionless surface.
The time interval between successive positions is 1 s.
a. What is the displacement of the ball after 3 s?
b. Where does the ball reach after 5 s?
c. After rolling for 7 s, the direction of motion of the ball is changed. It starts rolling toward its starting point.
Assume the coordinate system and the speed of the ball to remain unchanged. What is the displacement of
the ball between 7 s and 9 s?
45. 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
Position (m)
300
Swimmer A
250
200
150
100
50
–50
10
20
30
40
50
60
70
80
Time (s)
–100
46. The position-time graph of a pedestrian is given below. What is his displacement after 2.5 s?
12
Position (m)
10
8
6
4
2
–2
1
2
3
4
5
6
7
8
9
10
Time (s)
–4
–6
–8
47. What information is provided by the points on the line of a position-time graph of an object?
48. 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?
49. What are the two attributes of the coordinate system chosen for a motion diagram?
50. How is the time interval affected when the origin of the coordinate system of a motion diagram is changed?
51. What is the distance traveled by a vehicle in 12 minutes, if its speed is 35 km/h?
52. Given below is the position-time graph representing the motion of two friends, A and B, jogging in a park. Use
this graph to find their displacements after 4 s.
10
9
8
A
Position (m)
7
6
B
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
Time (s)
Problem
53. A body has a velocity of 72 km/hr. Find its value in m/s.
54. The velocity of sound in air is 332 m/s. If the unit of length is km and the unit of time is hour, what is the value
of velocity?
55. How many seconds are there in the month of February in a leap year?
Essay
56. Analyze the graph and answer the following questions.
a.
b.
c.
Name the independent and dependent variables in the graph.
Name the type of relationship between the variables.
Find the speed of the body.
57. An object has an initial velocity v and uniform acceleration a. If it covers a distance d, then its final velocity, v
, is given by the expression,
.
a. Does this equation give the correct unit of measurement of vf?
b. Is this a base unit or a derived unit?
c. Rewrite this equation to find the distance traveled in terms of initial velocity, final velocity, and
acceleration.
58. Consider the expression for the arithmetic operation, 0.652 km + 195 cm + 1800 cm.
a. Is any conversion required to do this operation?
b. Convert all the measurements to meters and then solve this expression.
c. How many significant digits are present in the obtained answer?
59. Jessica is using a micrometer screw (screw gauge) to measure the diameter of a wire. While recording the
measurements, she views the readings from different angles.
a. Is there any difference in the recorded values of the same measurement reading, when viewed from
different angles?
b. Name the phenomenon that causes this difference.
c. Does this affect the precision of a measurement made by the student?
60. While performing an experiment to find the value of acceleration due to gravity, g, Lee made observations for
the time period of a simple pendulum. He only changed the length of the pendulum and recorded different
values of time period as given in the table.
25
36
49
64
81
100
Length L of
pendulum in
cm
1.005 1.205
1.405 1.610
1.810
2.01
Time for one
oscillation
Time period T
in s
a. Is there any linear relationship between the values of length and time period of the simple pendulum?
b. The L-T graph is a straight line passing through the origin. Find the relationship between the length and
time period of the pendulum.
c. What are the units of the constant obtained as a ratio of L and T ?
61. 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?
62. Linda starts for her school at eight in the morning. There is a straight road that connects her house to the school.
She reaches school after 3.5 minutes. Her physics teacher has asked her to note her position after every 30
seconds on her way to school.
The values for her position (distance from her home) are listed with each time interval in the table below:
Time (in
seconds)
Position
(in
meters)
0
30
60
90
120
150
180
210
0
45
90
135
180
225
270
315
Using this position time table,
a. Draw a position-time graph to represent Linda’s motion from home to school.
b. Calculate the average velocity of Linda using the position-time graph.
c. What is the velocity of Linda on a return trip home if she reaches back home in the same time of 3.5
minutes? Assume Linda’s house to be the fixed origin of the graph.
63. A mouse is running at a high speed between the kitchen and storeroom, situated along the same line in a
building. A boy observes the mouse picking up pieces of bread from the kitchen and leaving them in a box in the
storeroom. The boy observes the positions of the mouse after fixed intervals. He finds that the mouse travels the
same displacement of 2.0 m in every half second. Starting from the door of the kitchen, the mouse reaches the
door of the storeroom in 3.0 s.
a. Make a position-time table for the motion of the mouse from the kitchen to the storeroom.
b. Draw the particle model of this motion.
c. Convert this model into the corresponding position-time graph.
64. Thomas cycles on a straight road near his house. After sometime, his sister Anna also starts cycling. Their
motions are represented by the position-time graphs given below.
a. How long had Thomas been cycling when Anna started cycling?
b. What is the position at which Anna crosses Thomas?
c. What is the difference between their positions after 5 s?
65. Three railway stations, A, B, and C, are situated on a straight railway route. Station B is at 30 km in the east
from station A and station C is at 60 km in east from station A. A train, with a constant average velocity, starts
from A and reaches B in 15 minutes, and reaches C in 30 minutes. Assuming that station A is the origin, find the
following:
a. The position of the train moving from station A to station B after 10 minutes.
b. The position of the train moving from station A to station B after 10 minutes, if station B is assumed to be
the origin.
c. The position of the train moving from station A to station B after 10 minutes, if station C is assumed to be
the origin.
66. 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.
1111
Answer Section
TRUE/FALSE
1. ANS: T
The position of a moving object in a selected coordinate system is the position of the object relative to the zero
of the coordinate system. The sign depends upon the object’s position relative to zero.
PTS: 1
DIF: 2
REF: Page 33
OBJ: 2.2.2 Recognize that the chosen coordinate system affects the sign of objects' positions.
NAT: B.4 | UCP.1
TOP: Recognize that the chosen coordinate system affects the sign of objects' positions.
KEY: Position
MSC: 2
NOT: /T/ Correct! /F/ The sign of an object's position depends upon its position with respect to the zero of the
coordinate system. The position of an object can also be negative.
2. ANS: F
The slope of the position-time graph of an object indicates the average velocity of the object.
PTS: 1
DIF: 1
REF: Page 44
OBJ: 2.4.2 Differentiate between speed and velocity.
NAT: B.4
TOP: Differentiate between speed and velocity.
KEY: Average velocity | Average speed
MSC: 1
NOT: /T/ The slope of a position-time graph of an object gives the average velocity of the object. /F/ Correct!
3. ANS: T
A time interval is a scalar quantity, because it needs only the magnitude for its complete description.
PTS: 1
DIF: 1
REF: Page 36
OBJ: 2.2.4 Determine a time interval.
NAT: B.4
TOP: Determine a time interval.
KEY: Time interval
MSC: 1
NOT: /T/ Correct! /F/ Time interval is a scalar quantity.
4. ANS: T
The slope of a straight line is a constant quantity. The average velocity of a moving object is the slope of the
straight line representing its position-time graph.
PTS:
OBJ:
TOP:
MSC:
NOT:
1
DIF: 1
REF: Page 44
2.3.1 Develop position-time graphs for moving objects.
NAT: B.4
Develop position-time graphs for moving objects.
KEY: Position-time graph
2
/T/ Correct! /F/ The straight line position-time graph represents the constant average velocity.
MULTIPLE CHOICE
5. ANS: B
10–6 is equivalent to the metric prefix micro (µ). Therefore, 1 micrometer (1 µm) = 10–6 m.
Feedback
A
B
The metric prefix milli (m) is equivalent to 10e–3 m.
Correct!
C
D
The metric prefix kilo (k) is equivalent to 10e+3 m.
The metric prefix mega (M) is equivalent to 10e+6 m.
PTS: 1
DIF: 2
TOP: Use the metric system.
6. ANS: A
Volume of a cube V = L3.
REF: Page 6
KEY: SI units
OBJ: 1.1.2 Use the metric system.
MSC: 1
Feedback
A
B
C
D
Correct!
Convert L into meters and then use the formula V = L* L* L to calculate the volume.
To calculate the volume, convert L into meters. Instead of squaring, take the cube of L.
Convert L into meters before cubing its value.
PTS: 1
DIF: 2
REF: Page 6
OBJ: 1.1.3 Evaluate answers using dimensional analysis.
TOP: Evaluate answers using dimensional analysis.
KEY: Dimensional analysis
MSC: 2
7. ANS: D
As per the common rules for counting significant figures: (i) All nonzero digits are significant. (ii) All zeros on
the right of the last nonzero digit in the decimal part are significant.
Feedback
A
B
C
D
All zeros on the right of the last nonzero digit in the decimal part are significant.
The last two zeros are also significant.
The last zero is also significant.
Correct!
PTS: 1
DIF: 2
REF: Page 7
OBJ: 1.1.4 Perform arithmetic operations using scientific notation.
TOP: Perform arithmetic operations using scientific notation.
KEY: Significant digits
MSC: 2
8. ANS: C
The pressure P is inversely proportional to the volume V. For inverse relation, the graph between the variables is
a hyperbola.
Feedback
A
B
C
D
P and V do not have a linear relationship.
P and V do not have a quadratic relationship.
Correct!
P and V have an inverse relationship, hence the graph is a hyperbola.
PTS:
OBJ:
TOP:
MSC:
9. ANS:
1
DIF: 2
REF: Page 18
1.3.3 Recognize common relationships in graphs.
Recognize common relationships in graphs.
3
D
. On squaring both sides we get,
.
KEY: Inverse relationship
Therefore, T2  L.
Feedback
A
B
C
D
T is inversely proportional to the square root of g.
T is directly proportional to the square root of L.
The square of T is inversely proportional to g.
Correct!
PTS: 1
DIF: 2
REF: Page 17
OBJ: 1.3.3 Recognize common relationships in graphs.
TOP: Recognize common relationships in graphs.
KEY: Linear relationship
MSC: 3
10. ANS: B
The slope is the ratio of the vertical change to the horizontal change.
Feedback
A
B
C
D
Reciprocate the ratio.
Correct!
PR is neither the vertical nor the horizontal change.
PR is the horizontal change and not the vertical change.
PTS: 1
DIF: 1
REF: Page 17
OBJ: 1.3.1 Graph the relationship between independent and dependent variables.
TOP: Graph the relationship between independent and dependent variables.
KEY: Slope
MSC: 2
11. ANS: D
Distance = speed  time
Substituting the values in the relation for distance, we get, d = (15.0 m/s)(12.0 min)(60 s/1 min) = 10,800 m
= 1.08  01 km
Feedback
A
B
C
D
Speed is multiplied with time to calculate the distance. All the quantities should have
units of the same system.
Time must be converted to seconds.
Time should be multiplied with speed, not divided, to calculate the distance.
Correct!
PTS: 1
DIF: 2
REF: Page 44
OBJ: 2.4.2 Differentiate between speed and velocity.
TOP: Differentiate between speed and velocity.
MSC: 2
12. ANS: C
Velocity and displacement are vector quantities.
Feedback
A
B
C
D
Speed and distance are scalar quantities.
Velocity is a vector, but distance is scalar.
Correct!
Displacement is a vector, but speed is scalar.
NAT: B.4
KEY: Average speed
PTS: 1
DIF: 1
REF: Page 35
OBJ: 2.2.3 Define displacement.
NAT: B.4
TOP: Define displacement.
KEY: Vectors
MSC: 1
13. ANS: A
When two displacement vectors have the same direction, their resultant has magnitude equal to the sum of their
magnitudes. The direction of the resultant is the same as the direction of the original vectors.
Feedback
A
B
C
D
Correct!
The resultant is the sum of the vectors, and not the difference of the vectors.
The resultant of two vectors, having the same direction, also has the same direction as the
original vectors.
The resultant is not perpendicular, but is in the direction of the original vectors.
PTS: 1
NAT: B.4
MSC: 2
DIF: 2
REF: Page 37
TOP: Define displacement.
OBJ: 2.2.3 Define displacement.
KEY: Displacement | Resultant
COMPLETION
14. ANS: dimensional
PTS:
OBJ:
TOP:
MSC:
15. ANS:
1
DIF: 1
REF: Page 6
1.1.3 Evaluate answers using dimensional analysis.
Evaluate answers using dimensional analysis.
1
significant digits
PTS:
OBJ:
TOP:
MSC:
16. ANS:
1
DIF: 1
REF: Page 7
1.1.4 Perform arithmetic operations using scientific notation.
Perform arithmetic operations using scientific notation.
KEY: Significant digits
1
linear
PTS:
OBJ:
TOP:
MSC:
17. ANS:
1
DIF: 1
REF: Page 16
1.3.3 Recognize common relationships in graphs.
Recognize common relationships in graphs.
2
slope
PTS: 1
DIF: 1
TOP: Interpret graphs.
REF: Page 17
KEY: Slope
KEY: Dimensional analysis
KEY: Linear relationship
OBJ: 1.3.2 Interpret graphs.
MSC: 1
18. ANS:
PTS:
OBJ:
TOP:
KEY:
1
DIF: 2
REF: Page 17
1.3.1 Graph the relationship between independent and dependent variables.
Graph the relationship between independent and dependent variables.
Slope
MSC: 2
19. ANS: particle
PTS:
OBJ:
NAT:
KEY:
20. ANS:
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: 1
REF: Page 33
2.1.2 Develop a particle model to represent a moving object.
UCP.2 | B.4 TOP: Develop a particle model to represent a moving object.
Particle model
MSC: 2
resultant
1
DIF: 1
REF: Page 35
2.2.5 Use a motion diagram to answer questions about an object's position or displacement.
B.4
Use a motion diagram to answer questions about an object's position or displacement.
Vectors | Resultant
MSC: 1
SHORT ANSWER
21. ANS:
a. Meter per second (m/s)
b. Derived unit
PTS: 1
DIF: 2
REF: Page 5
OBJ: 1.1.2 Use the metric system.
TOP: Use the metric system.
KEY: SI units
MSC: 1
22. ANS:
The number 5.0 indicates that the measurement is precise up to the first decimal place, whereas 5.00 indicates
that the measurement is precise up to the second decimal place.
PTS: 1
DIF: 2
REF: Page 12
OBJ: 1.2.1 Distinguish between accuracy and precision.
TOP: Distinguish between accuracy and precision.
KEY: Precision
MSC: 2
23. ANS:
The value m = 10.23 kg is more precise, being correct up to two decimal places.
PTS: 1
DIF: 2
REF: Page 7
OBJ: 1.2.1 Distinguish between accuracy and precision.
TOP: Distinguish between accuracy and precision.
KEY: Accuracy
MSC: 3
NOT: The significant digits in a number shows its precision.
24. ANS:
a. The body moves with uniform velocity.
b. The body moves with uniform acceleration.
c. The body moves with nonuniform acceleration.
PTS: 1
DIF: 3
REF: Page 16
OBJ: 1.3.2 Interpret graphs.
TOP: Interpret graphs.
KEY: Linear relationship
MSC: 3
25. ANS:
The conclusions that can be drawn if a velocity-time graph is parallel to the time axis are:
a. The body is moving with uniform velocity.
b. Its acceleration is zero.
c. Its displacement can be found by finding the area of the graph.
PTS: 1
DIF: 2
REF: Page 15
OBJ: 1.3.2 Interpret graphs.
TOP: Interpret graphs.
KEY: Independent and dependent variables
MSC: 2
26. ANS:
The conclusions that can be drawn if a velocity-time graph is a curve are:
a. The body has a variable velocity and variable acceleration.
b. The area under the curve represents displacement.
c. Acceleration at any instant can be found by finding the slope at that point.
PTS: 1
DIF: 2
REF: Page 15
OBJ: 1.3.2 Interpret graphs.
TOP: Interpret graphs.
KEY: Nonlinear relationship
MSC: 2
27. ANS:
In base units, 1 newton = 1 kg m/s2.
One newton is the force required to produce a constant acceleration of 1 m/s in an object of mass 1 kg, in the
direction of application of force.
PTS: 1
DIF: 2
REF: Page 5
OBJ: 1.1.2 Use the metric system.
TOP: Use the metric system.
KEY: SI units
MSC: 3
28. ANS:
A possible metric unit for volume is m3. It is a derived unit since it is created using a basic SI unit, meter.
PTS: 1
DIF: 2
TOP: Use the metric system.
29. ANS:
REF: Page 5
KEY: SI units
OBJ: 1.1.2 Use the metric system.
MSC: 1
The conversion factor used for converting 10 hours to seconds is
PTS:
OBJ:
TOP:
MSC:
30. ANS:
1
DIF: 1
REF: Page 6
1.1.3 Evaluate answers using dimensional analysis.
Evaluate answers using dimensional analysis.
2
KEY: Dimensional analysis
PTS: 1
DIF: 2
REF: Page 6
OBJ: 1.1.3 Evaluate answers using dimensional analysis.
TOP: Evaluate answers using dimensional analysis.
KEY: Dimensional analysis
MSC: 2
31. ANS:
Using scientific notation, the number 13900 can be expressed as 1.39  104. This number has three significant
digits.
PTS: 1
DIF: 2
REF: Page 7
OBJ: 1.1.4 Perform arithmetic operations using scientific notation.
TOP: Perform arithmetic operations using scientific notation.
KEY: Significant digits
MSC: 2
32. ANS:
Two-point calibration is the method of checking the accuracy of an instrument. In this method, an instrument is
checked for zero error and for the correctness of a reading, while measuring an accepted standard.
PTS: 1
DIF: 2
REF: Page 13
OBJ: 1.2.2 Determine the precision of measured quantities.
TOP: Determine the precision of measured quantities.
KEY: Accuracy
MSC: 2
33. ANS:
The position-time graphs of both runners show linear relationship between their positions and time. These
straight line graphs show that the runners have uniform speeds. The slopes of these lines of graphs give the
value of the speeds of the runners. The steeper the position-time graph of a runner, higher is his speed.
Therefore, Ian is the faster runner.
PTS: 1
DIF: 2
REF: Page 16
OBJ: 1.3.2 Interpret graphs.
TOP: Interpret graphs.
KEY: Linear relationship
MSC: 2
34. ANS:
The speed-time graph is a straight line parallel to the axis on which time is plotted. The values of acceleration
and displacement of the object in a given interval can be calculated from this graph.
PTS: 1
DIF: 2
REF: Page 16
OBJ: 1.3.3 Recognize common relationships in graphs.
TOP: Recognize common relationships in graphs.
KEY: Linear relationship
MSC: 2
35. ANS:
Motion diagram is a series of images showing the positions of a moving object at equal time intervals.
PTS: 1
DIF: 1
REF: Page 33
OBJ: 2.1.1 Draw motion diagrams to describe motion.
NAT: B.4
TOP: Draw motion diagrams to describe motion.
KEY: Motion diagram
MSC: 2
36. ANS:
A coordinate system tells about the location of the zero point of the variables defining the motion of the object
to be studied. The coordinate system also explains the direction in which the values of the variables increase.
PTS: 1
DIF: 1
REF: Page 34
OBJ: 2.2.1 Define coordinate systems for motion problems.
NAT: B.4 | UCP.1
TOP: Define coordinate systems for motion problems.
KEY: Coordinate system | Origin
MSC: 2
37. ANS:
Displacement is a vector quantity, while distance is a scalar quantity. Displacement has both the magnitude and
direction. Distance has only magnitude. The displacement of an object is equal to the difference between its
final position and initial position. When an object starts moving from a certain point and after covering certain
distance returns to its starting position, its displacement becomes zero.
PTS: 1
DIF: 2
REF: Page 37
OBJ: 2.2.3 Define displacement.
NAT: B.4
TOP: Define displacement.
KEY: Distance | Displacement | Scalars | Vectors
MSC: 2
38. ANS:
The equation of motion for average velocity is
. In this equation, d is the position of an object,
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.
is
PTS: 1
DIF: 1
REF: Page 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
39. ANS:
Average velocity of an object is defined as the change in position of the object moving along a straight line,
divided by the time during which the change occurred. In symbolic form, the average velocity
.
PTS: 1
DIF: 2
REF: Page 44
OBJ: 2.4.1 Define velocity.
NAT: B.4
TOP: Define velocity.
KEY: Average velocity
MSC: 2
40. ANS:
The straight line position-time graph of a moving object gives the information about the nature of the motion of
the object. It is also used to calculate the average velocity of the object. Since the graph is a straight line, the
object is undergoing uniform motion. The slope of this line gives the value of the average velocity of the object.
PTS: 1
DIF: 2
REF: Page 43
OBJ: 2.4.1 Define velocity.
NAT: B.4
TOP: Define velocity.
KEY: Average velocity
MSC: 2
41. ANS:
The average velocity of an object is equal to the slope of the line representing the position-time graph of the
object. In this graph, the slope of Ian’s line is steeper than the slope of Nick’s line. A steeper slope indicates a
greater change in displacement during each time interval. Average velocity for a given time interval is
proportional to the change in the displacement. Therefore, the average velocity of Ian is more than the average
velocity of Nick.
PTS: 1
DIF: 3
REF: Page 43
OBJ: 2.4.1 Define velocity.
NAT: B.4
TOP: Define velocity.
KEY: Average velocity
MSC: 2
42. ANS:
The position-time graph corresponding to this particle model is plotted below.
50
45
Position (m)
40
35
30
25
20
15
10
5
2
4
6
8
10
12
14
16
18
20
22
24
Time (s)
PTS: 1
DIF: 3
REF: Page 40
OBJ: 2.3.1 Develop position-time graphs for moving objects.
NAT: B.4
TOP: Develop position-time graphs for moving objects.
KEY: Position-time graph
MSC: 2
43. 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: 1
REF: Page 44
OBJ: 2.4.1 Define velocity.
NAT: B.4
TOP: Define velocity.
KEY: Displacement | Average velocity
MSC: 1
44. ANS:
a. The value of displacement after 3 s is 12 m.
b. After 5 s, the ball reaches at 20 m from its starting point.
c. The position of the ball after 7 s = 28 m.
The position of the ball after 9 s = 20 m.
The direction of the motion of the ball is reversed after 7 s. Therefore, the displacement of the ball between
7 s and 9 s = d = 20 – 28 = –8 m. The negative sign shows that the direction of displacement in this case is
negative, toward the starting point.
PTS: 1
DIF: 3
REF: Page 36
OBJ: 2.2.5 Use a motion diagram to answer questions about an object's position or displacement.
NAT: B.4
TOP: Use a motion diagram to answer questions about an object's position or displacement.
KEY: Displacement
MSC: 3
45. 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: 1
DIF: 2
REF: Page 38
OBJ: 2.2.4 Determine a time interval.
NAT: B.4
TOP: Determine a time interval.
KEY: Time interval | Origin
MSC: 2
46. ANS:
The position-time graph of the pedestrian intersects the x-axis at 2.5 s. Thus, the displacement in 2.5 s is –10 m.
PTS: 1
DIF: 2
REF: Page 38
OBJ: 2.3.2 Use a position-time graph to interpret an object's position or displacement.
NAT: B.4
TOP: Use a position-time graph to interpret an object's position or displacement.
KEY: Position-time graph | Displacement
MSC: 1
47. ANS:
The points on the line of a position-time graph of an object represent the most likely positions of the moving
object at the times between the recorded data points.
PTS:
OBJ:
NAT:
KEY:
48. ANS:
1
DIF: 2
REF: Page 38
2.3.2 Use a position-time graph to interpret an object's position or displacement.
B.4
TOP: Use a position-time graph to interpret an object's position or displacement.
Position-time graph | Position
MSC: 1
The resultant displacement is 2 units toward the east, and his position is at 2.
PTS: 1
DIF: 2
REF: Page 34
OBJ: 2.2.5 Use a motion diagram to answer questions about an object's position or displacement.
NAT: B.4
TOP: Use a motion diagram to answer questions about an object's position or displacement.
KEY: Displacement
MSC: 2
49. ANS:
The two attributes of the coordinate system chosen for a motion diagram are the origin and the axis of the
coordinate system.
PTS: 1
DIF: 2
REF: Page 34
OBJ: 2.2.5 Use a motion diagram to answer questions about an object's position or displacement.
NAT: B.4
TOP: Use a motion diagram to answer questions about an object's position or displacement.
KEY: Coordinate system | Origin
MSC: 2
50. ANS:
The time interval is a scalar quantity. Its value is not affected by the change in the relative position of the origin
of the coordinate system.
PTS: 1
DIF: 2
REF: Page 36
OBJ: 2.2.4 Determine a time interval.
NAT: B.4
TOP: Determine a time interval.
KEY: Time interval
MSC: 2
51. 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: 2
REF: Page 36
OBJ: 2.2.3 Define displacement.
NAT: B.4
TOP: Define displacement.
KEY: Distance
MSC: 2
52. ANS:
The displacements of A and B are the coordinates of the vertical line with their respective position-time graphs
at 4 s.
8
A
7
Position (m)
6
B
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
Time (s)
The value of displacement of A is approximately 4 m
The value of displacement of B is approximately 3 m.
PTS: 1
NAT: B.4
MSC: 1
DIF: 3
REF: Page 36
TOP: Define displacement.
OBJ: 2.2.3 Define displacement.
KEY: Displacement
PROBLEM
53. ANS:
PTS:
OBJ:
TOP:
MSC:
54. ANS:
1
DIF: 2
REF: Page 6
1.1.3 Evaluate answers using dimensional analysis.
Evaluate answers using dimensional analysis.
KEY: Dimensional analysis
2
NOT: 1 km = 1000 m and 1 hr = 60*60 s = 3600 s
PTS:
OBJ:
TOP:
MSC:
55. ANS:
1
DIF: 3
REF: Page 7
1.1.3 Evaluate answers using dimensional analysis.
Evaluate answers using dimensional analysis.
KEY: Dimensional analysis
2
NOT: 1 m =0.001 km and 1 s = 1/3600 hr
2505600 s
PTS: 1
DIF: 3
REF: Page 6
OBJ: 1.1.3 Evaluate answers using dimensional analysis.
TOP: Evaluate answers using dimensional analysis.
KEY: Dimensional analysis
MSC: 2
NOT: In a leap year, in the month of February, there are 29 days. Therefore, the number of seconds =
29*24*60*60 = 2505600 s.
ESSAY
56. ANS:
a.
Time is the independent variable and distance is the dependent variable.
b.
Linear relationship exists between the variables.
c.
PTS: 1
DIF: 3
REF: Page 16
OBJ: 1.3.1 Graph the relationship between independent and dependent variables.
TOP: Graph the relationship between independent and dependent variables.
KEY: Independent and dependent variables
MSC:
3
57. ANS:
a. To find the unit of measurement of v , substitute the units of d, a, and v .
The unit of
is m2/s2.
Therefore, the unit of v is m/s, which is the correct unit for the measurement of velocity.
b. The unit of measuring velocity is a derived unit. It is created using two basic SI units, meter and second.
c. The equation for finding distance is
.
PTS: 1
DIF: 3
REF: Page 6 | Page 7
OBJ: 1.1.3 Evaluate answers using dimensional analysis.
TOP: Evaluate answers using dimensional analysis.
KEY: Dimensional analysis
MSC: 2
58. ANS:
a. To solve any arithmetic operation involving physical quantities, all the quantities involved should have the
measurement units of the same system of units. In this expression, 0.615 km should be first converted to cm,
or magnitudes in cm should be converted to km.
b. 0.652 km = 652 m, 195 cm = 1.95 m, 1800 cm = 18 m
Therefore, 0.652 km + 195 cm + 1800 cm becomes 652 m + 1.95 m + 18 m = 672 m
c. The number has three significant digits.
PTS: 1
DIF: 3
REF: Page 6
OBJ: 1.1.4 Perform arithmetic operations using scientific notation.
TOP: Perform arithmetic operations using scientific notation.
KEY: Significant digits
MSC: 1
59. ANS:
a. The recorded values of the same measurement reading differ when the reading is viewed from different
angles.
b. The phenomenon that causes this difference is called parallax.
c. Parallax does not affect the precision of a measurement, but it affects the accuracy of the measurements.
PTS: 1
DIF: 3
REF: Page 13
OBJ: 1.2.2 Determine the precision of measured quantities.
TOP: Determine the precision of measured quantities.
KEY: Accuracy | Precision
MSC: 3
60. ANS:
a. The time period of a simple pendulum increases with length. However, from the readings given in the table,
it is clear that T is not proportional to L.
b. The straight line graph in case of L-T graph shows that L is directly proportional to T .
c. Since
, therefore
= constant. The units of this constant are m/s .
PTS: 1
DIF: 3
REF: Page 16 | Page 17
OBJ: 1.3.3 Recognize common relationships in graphs.
TOP: Recognize common relationships in graphs.
KEY: Linear relationship | Nonlinear relationship
MSC: 3
61. 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: 1
DIF: 3
REF: Page 44
OBJ: 2.4.2 Differentiate between speed and velocity.
NAT: B.4
TOP: Differentiate between speed and velocity.
KEY: Average speed | Average velocity
MSC: 2
62. ANS:
a. The position-time graph of Linda’s motion from home to school is as follows:
315
Position (m)
270
225
180
135
90
45
30
60
90 120 150 180 210 240
Time (s)
b. Average velocity of Linda = Slope of the above graph =
c. During her return journey from school, the average velocity of Linda is –1.5 m/s.
PTS: 1
DIF: 3
REF: Page 43
OBJ: 2.4.1 Define velocity.
NAT: B.4
TOP: Define velocity.
KEY: Average velocity
MSC: 3
63. ANS:
a. The position-time table for the motion of the mouse from the kitchen to the store is:
Position vs Time
Time (s)
Position (m)
0.0
0.0
0.5
2.0
1.0
4.0
1.5
6.0
2.0
2.5
3.0
8.0
10.0
12.0
b. The following particle model represents the motion of the mouse from the kitchen to the store.
Kitchen
Store
The time interval between two successive dots is of 0.5 s.
c. The position-time graph corresponding to the position-time table formed in part a, is plotted below.
PTS: 1
DIF: 3
REF: Page 40
OBJ: 2.3.3 Make motion diagrams, pictorial representations, and position-time graphs that are equivalent
representations describing an object's motion.
NAT: B.4
TOP: Make motion diagrams, pictorial representations, and position-time graphs that are equivalent
representations describing an object's motion.
KEY: Position-time graph
MSC: 2
64. ANS:
a. Thomas had been cycling for 1.0 s, when Anna started cycling.
b. Anna crosses Thomas at a point 12.0 m from the starting point.
c. Displacement of Thomas after 5.0 s = 20.0 m – 0.0 m = 20.0 m.
Displacement of Anna after 5.0 s = 24.0 m – 0.0 m = 24.0 m.
The difference in their positions after 5.0 s is 4.0 m with Anna being ahead.
PTS: 1
DIF: 3
REF: Page 42
OBJ: 2.3.2 Use a position-time graph to interpret an object's position or displacement.
NAT: B.4
TOP: Use a position-time graph to interpret an object's position or displacement.
KEY: Position-time graph | Instantaneous position
MSC: 2
65. ANS:
a. The position of the train is 20 km in the east to station A.
b. The position of the train becomes –10 km.
c. The position of the train becomes –40 km.
PTS:
OBJ:
NAT:
TOP:
KEY:
66. ANS:
a.
1
DIF: 3
REF: Page 35
2.2.2 Recognize that the chosen coordinate system affects the sign of objects' positions.
B.4 | UCP.1
Recognize that the chosen coordinate system affects the sign of objects' positions.
Coordinate system | Position | Origin
MSC: 3
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: 3
REF: Page 38
2.3.1 Develop position-time graphs for moving objects.
Develop position-time graphs for moving objects.
Displacement | Position-time graph | Average velocity
NAT: B.4
MSC: 2