Deck 1: Units, Physical Quantities, and Vectors

Question 1

If A > B, under what condition is | - | = A - B?

A) The statement is never true.
B) Vectors and are in opposite directions.
C) Vectors and are in the same direction.
D) Vectors and are in perpendicular directions.
E) The statement is always true.

Answer 1

Vectors and are in the same direction.

Question 2

Scientists use the metric system chiefly because it is more accurate than the English system.

Answer 2

False

Question 3

If an operatic aria lasts for 5.75 min, its length expressed in seconds is x s, where x is

A) less than 5.75.
B) greater than 5.75.

Answer 3

greater than 5.75.

Question 4

The current definition of the standard meter of length is based on

A) the distance between the earth's equator and north pole.
B) the distance between the earth and the sun.
C) the distance traveled by light in a vacuum.
D) the length of a particular object kept in France.

Question 5

Under what condition is | - | = A + B?

A) The magnitude of vector is zero.
B) Vectors and are in opposite directions.
C) Vectors and are in the same direction.
D) Vectors and are in perpendicular directions.
E) The statement is never true.

Question 6

When adding two numbers, the number of significant figures in the sum is equal to the number of significant figures in the least accurate of the numbers being added.

Question 7

When determining the number of significant figures in a number, zeroes to the left of the decimal point are never counted.

Question 8

If - = 0, then the vectors and have equal magnitudes and are directed in the opposite directions from each other.

Question 9

If the eastward component of vector is equal to the westward component of vector
And their northward components are equal. Which one of the following statements about these two vectors is correct?

A) Vector is parallel to vector .
B) Vectors and point in opposite directions.
C) Vector is perpendicular to vector .
D) The magnitude of vector is equal to the magnitude of vector .
E) The magnitude of vector is twice the magnitude of vector .

Question 10

Which of the following is an accurate statement?

A) The magnitude of a vector can be zero even though one of its components is not zero.
B) It is possible to add a scalar quantity to a vector.
C) Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero.
D) Rotating a vector about an axis passing through the tip of the vector does not change the vector.
E) The magnitude of a vector is independent of the coordinate system used.

Question 11

If the magnitude of vector
is less than the magnitude of vector
, then the x component of
is less than the x component of .

Question 12

The current definition of the standard kilogram of mass is based on

A) the mass of the earth.
B) the mass of the sun.
C) the mass a particular object kept in France.
D) the mass of a cesium-133 atom.

Question 13

The magnitude of a vector can never be less than the magnitude of one of its components.

Question 14

The current definition of the standard second of time is based on

A) the frequency of radiation emitted by cesium atoms.
B) the earth's rotation rate.
C) the duration of one year.
D) the oscillation of a particular pendulum kept in France.

Question 15

For the vectors shown in the figure, express vector
in terms of vectors and .

Question 16

If a tree is 15 m tall, its height expressed in feet is x ft, where x is

A) less than 15.
B) greater than 15.

Question 17

If the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other.

Question 18

If a woman weighs 125 lb, her mass expressed in kilograms is x kg, where x is

A) less than 125.
B) greater than 125.

Question 19

If a flower is 6.5 cm wide, its width expressed in millimeters is x mm, where x is

A) less than 6.5.
B) greater than 6.5.

Question 20

If all the components of a vector are equal to 1, then that vector is a unit vector.

Question 21

Convert 1.2 × 10^-3 to decimal notation.

A) 1.200
B) 0.1200
C) 0.0120
D) 0.0012
E) 0.00012

Question 22

0.0001776 can also be expressed as

A) 1.776 × 10^-3.
B) 1.776 × 10^-4.
C) 17.72 × 10⁴.
D) 1772 × 10⁵.
E) 177.2 × 10⁷.

Question 23

What is the difference between 103.5 and 102.24 written with the correct number of significant figures?

A) 1
B) 1.3
C) 1.26
D) 1.260
E) 1.2600

Question 24

What is the sum of 1.53 + 2.786 + 3.3 written with the correct number of significant figures?

A) 8
B) 7.6
C) 7.62
D) 7.616
E) 7.6160

Question 25

If, in a parallel universe, π has the value 3.14149, express π in that universe to four significant figures.

A) 3.141
B) 3.142
C) 3.1415
D) 3.1414

Question 26

0.00325 × 10^-8 cm can also be expressed in mm as

A) 3.25 × 10^-12 mm.
B) 3.25 × 10^-11 mm.
C) 3.25 × 10-¹⁰ mm.
D) 3.25 × 10^-9 mm.
E) 3.25 × 10^-8 mm.

Question 27

What is the result of 1.58 ÷ 3.793 written with the correct number of significant figures?

A) 4.1656 × 10^-1
B) 4.166 × 10^-1
C) 4.17 × 10^-1
D) 4.2 × 10^-1
E) 4 × 10^-1

Question 28

Write out the number 7.35 × 10^-5 in full with a decimal point and correct number of zeros.

A) 0.00000735
B) 0.0000735
C) 0.000735
D) 0.00735
E) 0.0735

Question 29

If two vectors are perpendicular to each other, their cross product must be zero.

Question 30

What is the sum of 1123 and 10.3 written with the correct number of significant figures?

A) 1.13 × 10³
B) 1133.3000
C) 1.1 × 10³
D) 1133.3
E) 1133

Question 31

The number 0.003010 has

A) 7 significant figures.
B) 6 significant figures.
C) 4 significant figures.
D) 2 significant figures.

Question 32

The value of the dot product of two vectors depends on the particular coordinate system being used.

Question 33

What is the value of π(8.104)², written with the correct number of significant figures?

A) 206.324
B) 206.323
C) 206.3
D) 206
E) 200

Question 34

What is 56 + (32.00) / (1.2465 + 3.45) written with the correct number of significant figures?

A) 62.8
B) 62.812
C) 62.81
D) 63
E) 62.8123846

Question 35

What is the product of 11.24 and 1.95 written with the correct number of significant figures?

A) 22
B) 21.9
C) 21.92
D) 21.918
E) 21.9180

Question 36

If two vectors point in opposite directions, their cross product must be zero.

Question 37

What is to the proper number of significant figures?

A) 0.91
B) 0.911
C) 0.9108
D) 0.9

Question 38

If two nonzero vectors point in the same direction, their dot product must be zero.

Question 39

What is 34 + (3) × (1.2465) written with the correct number of significant figures?

A) 37.7
B) 37.74
C) 4 × 10¹
D) 38
E) 37.7395

Question 40

If and
Are nonzero vectors for which ∙ = 0, it must follow that

A) × = 0.
B) is parallel to .
C) | × | = AB.
D) | × | = 1.

Question 41

The length and width of a rectangle are 1.125 m and 0.606 m, respectively. Multiplying, your calculator gives the product as 0.68175. Rounding properly to the correct number of significant figures, the area should be written as

A) 0.7 m².
B) 0.68 m²
C) 0.682 m²
D) 0.6818 m²
E) 0.68175 m²

Question 42

Convert a speed of 4.50 km/h to units of ft/min. (1.00 m = 3.28 ft)

A) 0.246 ft/min
B) 82.3 ft/min
C) 165 ft/min
D) 246 ft/min
E) 886 ft/min

Question 43

Approximately how many times does an average human heart beat in a year?

A) 4 × 10⁵
B) 4 × 10⁶
C) 4 × 10⁷
D) 4 × 10⁸
E) 4 × 10⁹

Question 44

What is 0.205^2/3, expressed to the proper number of significant figures?

A) 0.348
B) 0.35
C) 0.3
D) 0.3477

Question 45

How many nanoseconds does it take for a computer to perform one calculation if it performs 6.7 × 10⁷ calculations per second?

A) 15 ns
B) 67 ns
C) 11 ns
D) 65 ns

Question 46

In addition to 1 m = 39.37 in., the following exact conversion equivalents are given: 1 mile = 5280 ft, 1 ft = 12 in, 1 hour = 60 min, and 1 min = 60 s. If a particle has a velocity of 8.4 miles per hour, its velocity, in m/s, is closest to

A) 3.8 m/s.
B) 3.0 m/s.
C) 3.4 m/s.
D) 4.1 m/s.
E) 4.5 m/s.

Question 47

A person on a diet loses 1.6 kg in a week. How many micrograms/second (μg/s) are lost?

A) 2.6 × 10³ μg/s
B) 1.6 × 10⁵ μg/s
C) 44 μg/s
D) 6.4 × 10⁴ μg/s

Question 48

Albert uses as his unit of length (for walking to visit his neighbors or plowing his fields) the albert (A), the distance Albert can throw a small rock. One albert is 92 meters. How many square alberts is equal to one acre? (1 acre = 43,560 ft2 = 4050 m²)

Question 49

A certain CD-ROM disk can store approximately 6.0 × 10² megabytes of information, where 106 bytes = 1 megabyte. If an average word requires 9.0 bytes of storage, how many words can be stored on one disk?

A) 6.7 × 10⁷ words
B) 5.4 × 10⁹ words
C) 2.1 × 10⁷ words
D) 2.0 × 10⁹ words

Question 50

The shortest wavelength of visible light is approximately 400 nm. Express this wavelength in centimeters.

A) 4 × 10^-5 cm
B) 4 × 10^-7 cm
C) 4 × 10^-9 cm
D) 4 × 10^-11 cm
E) 400 × 10^-11 cm

Question 51

Approximately how many times does an average human heart beat in a lifetime?

A) 3 × 10¹¹
B) 3 × 10¹⁰
C) 3 × 10⁹
D) 3 × 10⁸
E) 3 × 10⁷

Question 52

The wavelength of a certain laser is 0.35 micrometers, where 1 micrometer = 1 × 10^-6 m. Express this wavelength in nanometers.

A) 3.5 × 10² nm
B) 3.5 × 10³ nm
C) 3.5 × 10¹ nm
D) 3.5 × 10⁴ nm

Question 53

The mass of a typical adult woman is closest to

A) 20 kg.
B) 35 kg.
C) 75 kg.
D) 150 kg.

Question 54

A weight lifter can bench press 171 kg. How many milligrams (mg) is this?

A) 1.71 × 10⁸ mg
B) 1.71 × 10⁹ mg
C) 1.71 × 10⁷ mg
D) 1.71 × 10⁶ mg

Question 55

Add 3685 g and 66.8 kg and express your answer in milligrams (mg).

A) 7.05 × 10⁷ mg
B) 7.05 × 10⁴ mg
C) 7.05 × 10⁵ mg
D) 7.05 × 10⁶ mg

Question 56

The exhaust fan on a typical kitchen stove pulls 600 CFM (cubic feet per minute) through the filter. Given that 1.00 in. = 2.54 cm, how many cubic meters per second does this fan pull?

A) 0.283 m³/sec
B) 0.328 m³/sec
C) 3.05 m³/sec
D) 32.8 m³/sec

Question 57

The following exact conversion equivalents are given: 1 m = 100 cm, 1 in = 2.54 cm, and 1 ft + 12 in. If a computer screen has an area of 1.27 ft², this area is closest to

A) 0.00284 m².
B) 0.0465 m².
C) 0.118 m²
D) 0.284 m²
E) 4.65 m².

Question 58

A plot of land contains 5.8 acres. How many square meters does it contain?
[1 acre = 43,560 ft²]

A) 2.3 × 10⁴ m²
B) 7.1 × 10³ m²
C) 7.0 × 10⁴ m²
D) 5.0 × 10⁴ m²

Question 59

Express (4.3 × 10⁶)^-1/2 in scientific notation.

A) 4.8 × 10^-4
B) 2.1 × 10³
C) 2.1 × 10^-5
D) 2.1 × 10⁴

Question 60

The height of the ceiling in a typical home, apartment, or dorm room is closest to

A) 100 cm.
B) 200 cm.
C) 400 cm.
D) 500 cm.

Question 61

Vectors and
Are shown in the figure. Vector
Is given by = - ) The magnitude of vector Is 16.0 units, and the magnitude of vector Is 7.00 units. What is the magnitude of vector ?

A) 9.00
B) 9.53
C) 15.5
D) 16.2
E) 17.5

Question 62

Vector has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis. What are the x and y components of vector )

A) A_x = 3.83 and A_y = 3.21
B) A_x = 3.83 and A_y = -3.21
C) A_x = -3.21 and A_y = -3.83
D) A_x = -3.21 and A_y = 3.83
E) A_x = 4.29 and A_y = 2.16

Question 63

A helicopter is flying horizontally with a speed of 444 m/s over a hill that slopes upward with a 2% grade (that is, the "rise" is 2% of the "run"). What is the component of the helicopter's velocity perpendicular to the sloping surface of the hill?

A) 8.9 m/s
B) 220 m/s
C) 435 m/s
D) 444 m/s

Question 64

Estimate the number of times the earth will rotate on its axis during a human's lifetime.

A) 3 × 10⁴
B) 3 × 10⁵
C) 3 × 10⁶
D) 3 × 10⁷
E) 3 x 10⁸

Question 65

The components of vector are B_x = -3.5 and B_y = -9.7, and the components of vector
Are C_x = -6 and C_y = +8.1. What is the angle (less than 180 degrees) between vectors
And ?

A) 124°
B) 56°
C) 17°
D) 163°
E) 106°

Question 66

The components of vector are A_x = +2.2 and A_y = -6.9, and the components of vector
Are given are B_x = -6.1 and B_y = -2.2. What is the magnitude of the vector - ?

A) 9.5
B) 6.1
C) 9.9
D) 91
E) 0.76

Question 67

You walk 53 m to the north, then turn 60° to your right and walk another 45 m. Determine the direction of your displacement vector. Express your answer as an angle relative to east.

A) 63° N of E
B) 50° N of E
C) 57° N of E
D) 69° N of E

Question 68

The speed of a wave pulse on a string depends on the tension, F, in the string and the mass per unit length, μ, of the string. Tension has SI units of kg · m · s^-2 and the mass per unit length has SI units of kg · m^-1. What combination of F and μ must the speed of the wave be proportional to?

A) F / μ
B) μ / F
C)
D)
E)

Question 69

You walk 55 m to the north, then turn 60° to your right and walk another 45 m. How far are you from where you originally started?

A) 87 m
B) 50 m
C) 94 m
D) 46 m

Question 70

The components of vector are A_x = + 3.90 and A_y = -4.00. What is the angle measured counterclockwise from the +x-axis to vector
?

A) 314°
B) 134°
C) 224°
D) 136°
E) 46.0°

Question 71

Estimate the number of pennies that would fit in a box one foot long by one foot wide by one foot tall.

A) 5 × 10²
B) 5 × 10³
C) 5 × 10⁴
D) 5 × 10⁵
E) 5 x 10⁶

Question 72

Vector
has a magnitude of 5.5 cm and points along the x-axis. Vector
has a magnitude of 7.5 cm and points at +30° above the negative x-axis.
(a) Determine the x and y components of Vector .
(b) Determine the x and y components of Vector .
(c) Determine x and y components of the sum of these two vectors.
(d) Determine the magnitude and direction of the sum of these two vectors.

Question 73

The position x, in meters, of an object is given by the equation x = A + Bt + Ct², where t represents time in seconds. What are the SI units of A, B, and C?

A) m, m, m
B) m, s, s
C) m, s, s²
D) m, m/s, m/s²
E) m/s, m/s², m/s³

Question 74

Approximately how many pennies would you have to stack to reach an average 8-foot ceiling?

A) 2 × 10²
B) 2 × 10³
C) 2 × 10⁴
D) 2 × 10⁵
E) 2 x 10⁶

Question 75

A marathon is 26 mi and 385 yd long. Estimate how many strides would be required to run a marathon. Assume a reasonable value for the average number of feet/stride.

A) 4.5 × 10⁴ strides
B) 4.5 × 10³ strides
C) 4.5 × 10⁵ strides
D) 4.5 × 10⁶ strides

Question 76

An apple falls from an apple tree growing on a 20° slope. The apple hits the ground with an impact velocity of 16.2 m/s straight downward. What is the component of the apple's impact velocity parallel to the surface of the slope?

A) 5.5 m/s
B) 8.7 m/s
C) 12 m/s
D) 15 m/s

Question 77

Vector
has a magnitude of 75.0 cm and points at 30° above the positive x-axis. Vector
has a magnitude of 25.0 cm and points along the negative x-axis. Vector
has a magnitude of 40.0 cm and points at 45° below the negative x-axis.
(a) Determine the x and y components of Vector .
(b) Determine the x and y components of Vector .
(c) Determine the x and y components of Vector .
(d) Determine x and y components of the sum of these three vectors.
(e) Determine the magnitude and direction of the sum of these three vectors.

Question 78

A rabbit trying to escape a fox runs north for 8.0 m, darts northwest for 1.0 m, then drops 1.0 m down a hole into its burrow. What is the magnitude of the net displacement of the rabbit?

A) 8.8 m
B) 8.1 m
C) 66 m
D) 10 m

Question 79

The period of a pendulum is the time it takes the pendulum to swing back and forth once. If the only dimensional quantities that the period depends on are the acceleration of gravity, g, and the length of the pendulum, ℓ, what combination of g and ℓ must the period be proportional to? (Acceleration has SI units of m ∙ s^-2.).

A) g/ℓ
B) gℓ2
C) gℓ
D)
E)

Question 80

Vectors and Are shown in the figure. Vector Is given by = - ) The magnitude of vector Is 16.0 units, and the magnitude of vector Is 7.00 units. What is the angle of vector , measured counterclockwise from the +x-axis?

A) 16.9°
B) 22.4°
C) 73.1°
D) 287°
E) 292°