Deck 1: Space, Time, and Mass

Question 1

To describe the motion of a particle, one needs to specify

A) its position.
B) the time at which the particle has a certain position.
C) its position and the time at which it has this position.
D) its position in a certain reference frame and the time at which it has this position.

Answer 1

its position in a certain reference frame and the time at which it has this position.

Question 2

Two witnesses to a car accident are asked to testify in court. Here are their statements:
Witness 1: I was standing at the pedestrian crossing at Blue Square when the car in question was moving at high speed toward the left.
Witness 2: I was standing at the pedestrian crossing at Blue Square when the car in question was moving at high speed toward the right. Do the witnesses contradict each other?

A) Definitely yes.
B) Definitely no.
C) It depends on the reference frame adopted by each of the witnesses.

Answer 2

It depends on the reference frame adopted by each of the witnesses.

Question 3

Two physics students carefully measure the position of an object and report the following results:
Student 1: To get to the object, one should go 3.0 m north and then 4.0 m east.
Student 2: To get to the object, one should go 6.0 m south. Which one of the students is correct?

A) Student 1 only.
B) Student 2 only.
C) Either student 1 or student 2, but not both, depending on the reference frame chosen by each of the students.
D) Both student 1 and student 2 could be right, depending on the reference frame chosen by each of the students.
E) Neither student 1 nor student 2, irrespective of the choice of the reference frames.

Answer 3

Both student 1 and student 2 could be right, depending on the reference frame chosen by each of the students.

Question 4

In the international system of units (SI), the official unit of length is the

A) millimeter.
B) centimeter.
C) meter.
D) kilometer.
E) none of the above.

Question 5

Which of the following units is not a fundamental unit in the international system of units?

A) meter
B) kilogram
C) hour
D) all of the above
E) none of the above

Question 6

An acceptable (though perhaps unusual) unit for density is

A) kilogram/liter.
B) gram/centimeter³.
C) pound/gallon.
D) kilogram/meter³.
E) all of the above.

Question 7

Assume the following relationship between these two hypothetical volume units: 2 "squirts" = 7 "drips." The number of "squirts" in one "drip" is

A) 1/7.
B) 2/7.
C) 7.
D) 7/2.
E) 7/1.

Question 8

Assume the following relationship between two hypothetical volume units: 2 "squirts" = 7 "drips." The number of "drips" in one "squirt" is

A) 1/7.
B) 2/7.
C) 7.
D) 7/2.
E) 7/1.

Question 9

The number of angstroms (1 angstrom = 10^-10 m) in 5 fermi (1 fermi = 10^-15 m) is

A) 5 $\times$ 10^-5.
B) 5 $\times$ 10^-4.
C) 2 $\times$ 10^-5.
D) 2 $\times$ 10⁺⁴.
E) 5 $\times$ 10⁺⁵.

Question 10

20/20 vision is a term used to express normal visual acuity (the clarity or sharpness of vision) measured at a distance of 20 feet. If you have 20/20 vision, you can see clearly at 20 feet what should normally be seen at that distance. In European countries (that use the international system of units), the equivalent of 20/20 vision is

A) 6/6 vision
B) 7/7 vision.
C) 10/10 vision.
D) 40/40 vision.
E) 60/60 vision.

Question 11

Pararescue jumpers leave the helicopter when it is flying "10 and 10," meaning that the helicopter is 10 ft above the water and moving at a speed of 10 knots (1 knot = 1 nautical mi/h = 1.852 km/h). The international system of units equivalent of "10 and 10" is

A) 3 and 5.
B) 3 and 19.
C) 10 and 19.
D) 30 and 31.
E) 30 and 37.

Question 12

The maximum speed limit on certain highways is 70 mi/h in the United States and 120 km/h in Europe. The highest speed limit is

A) in Europe.
B) in the United States.
C) the same in both regions.

Question 13

All of the following inequalities for length units are correct except

A) 1 yard > 1 meter.
B) 1 mile > 1 kilometer.
C) 1 inch > 1 centimeter.
D) 1 foot > 10 centimeters.
E) 1 meter > 1 foot.

Question 14

All of the following inequalities for time units are correct except

A) 1 millisecond > 1 nanosecond.
B) 1 nanosecond > 1 microsecond.
C) 1 second > 1 millisecond.
D) 1 hour > 1000 seconds.
E) 1 minute > 10 seconds.

Question 15

All of the following inequalities for length units are correct except

A) 1 millimeter > 1 centimeter.
B) 1 meter > 1 millimeter.
C) 1 kilometer > 1 meter.
D) 1 centimeter > 1 micron.
E) 1 picometer > 1 nanometer.

Question 16

The most precise scientific standard of mass is based on

A) a specified fraction of the mass of the Earth.
B) the mass of a specific piece of material kept at special conditions.
C) a property of a particular kind of atom.
D) the speed of light.
E) an iron atom.

Question 17

All of the following "equalities" are approximately true (that is, are within a factor of two of being exact) except

A) 2 centimeters = 1 inch.
B) 2 kilometers = 1 mile.
C) 2 meters = 1 foot.
D) 2 liters = 1 gallon.
E) 2 pounds = 1 kilogram.

Question 18

The most precise scientific standard of length is based on

A) a specified fraction of the distance from the pole to the equator on Earth.
B) the distance separating two marks on a bar carefully kept at special conditions.
C) a property of a particular kind of atom.
D) the diameter of our Galaxy.
E) the speed of light in a vacuum.

Question 19

The most precise scientific standard of time is based on

A) a specified fraction of the mean solar day.
B) the time taken for a specific "seconds" pendulum kept at special conditions to complete one oscillation.
C) a property of a particular kind of atom.
D) the speed of light.
E) the travel time of light from the nearest star.

Question 20

Which mass is the largest?

A) 0.0231 kg
B) 2.31 $\times$ 10^-2 kg
C) 231 $\times$ 10^-4 kg
D) 23.1 g
E) They all represent the same mass.

Question 21

If 1 in. is approximately equal to 2.5 cm, then 1.0 in.² of surface area is approximately

A) 1/(6.3) cm².
B) 1/(2.5) cm².
C) 1.0 cm².
D) 2.5 cm².
E) 6.3 cm².

Question 22

If 1 in. is approximately equal to 2.5 cm, then 1.0 cm² of surface area is approximately

A) 1/(6.3) in².
B) 1/(2.5) in².
C) 1.0 in².
D) 2.5 in².
E) 6.3 in².

Question 23

If 1/3 yard is equal to 1 foot, then 1 cubic yard of volume is equal to

A) 1 cubic foot.
B) 3 cubic feet.
C) 9 cubic feet.
D) 27 cubic feet.
E) 81 cubic feet.

Question 24

A box is 1.5 yard wide, 1.2 feet wide and 3.5 in. high. Its volume in SI units is

A) 4.5 $\times$ 10^-2 m³.
B) 4.5 m³.
C) 1.5 $\times$ 10^-2 m³.
D) 1.5 $\times$ 10^-1 m³.
E) 3.0 $\times$ 10³ m³.

Question 25

The position of an object as a function of time is given by the equation x(t) = at² + bt + c. The dimensions of a, b, and c are

A) distance, distance, and distance.
B) distance/time, distance/time, and distance/time.
C) distance, distance/time, and distance/time².
D) distance·time², distance·time, distance.
E) distance/time², distance/time, distance.

Question 26

The position of an object as a function of time is given by the equation x(t) = asin(bt² + c). The dimensions of a, b, and c are

A) distance, angle, and angle.
B) distance, angle/time, and angle.
C) distance, angle/time², and angle/time².
D) distance, angle/time², and angle.
E) angle, angle/time², and angle.

Question 27

The speed of an object as a function of time is given by the equation v(t) = at² be^-ct. The dimensions of a, b, and c are -

A) distance/time, distance/time, and 1/time.
B) distance/time, distance/time, and time.
C) distance, distance/time, and 1/time.
D) distance/time³, distance/time, 1/time.
E) distance/time³, distance/time, time.

Question 28

If in the international system of units the variables a, b, and c are related to each other through the equation a^x = b^yc^z, and [c]_SI = s, [b]_SI = m/s, and [a]_SI = m/s², the powers x, y, and z that make the equation dimensionally consistent are

A) 1, 1, and -1.
B) -1, -1, and 1.
C) 2, 2, and -2.
D) all of the above.
E) none of the above.

Question 29

If in the international system of units $[ x ] _ { \mathrm { SI } } = \mathrm { m } , [ t ] _ { \mathrm { SI } } = \mathrm { s } , [ v ] _ { \mathrm { SI } } = \mathrm { m } / \mathrm { s }$ , and $[ a ] _ { \mathrm { SI } } = \mathrm { m } / \mathrm { s } ^ { 2 }$ , and (i) $x$ $= v t + a$ , (ii) $x = \frac { 1 } { 2 } a t ^ { 2 }$ , and (iii) $t = \left( \frac { 2 x } { a } \right) ^ { \frac { 1 } { 2 } }$ , the dimensionally consistent equation(s) is(are):

A) (i), (ii), and (iii).
B) (i) and (iii).
C) (i) and (ii).
D) (ii) and (iii).
E) only (i).

Question 30

The number of significant figures in 23.410 kg is

A) 2.
B) 3.
C) 4.
D) 5.
E) none of the above.

Question 31

The number of significant figures in 0.0213 kg is

A) 1.
B) 2.
C) 3.
D) 4.
E) 5.

Question 32

Which of the following represents a measurement with four significant figures?

A) 0.0231 kg
B) 1.2249 kg
C) 2256.23 kg
D) 11.40 kg
E) 1154.0 kg

Question 33

The volume of a cube of side 4.26 cm is

A) 77.308 $\times$ 10⁺⁶ m³.
B) 77.3 $\times$ 10⁺⁶ m³.
C) 77 m³.
D) 77.3 $\times$ 10^-6 m³.
E) 77.308 $\times$ 10^-6 m³.

Question 34

The sum of 1.00 m + 1531 mm + 2.54 $\times$ 10^-2 km, with the correct number of significant figures is

A) 0.3 $\times$ 10² m.
B) 27 m.
C) 27.9 m.
D) 27.93 m.
E) 27.931 m.

Question 35

The difference between 134.2 km and 4.782 km is

A) 129.4180 km.
B) 129.418 km.
C) 129.42 km.
D) 129.4 km.
E) 129 km.

Question 36

The density of a block is defined as the ratio of the block's mass to its volume. If the mass and the volume of a block were measured to be 123.34 kg and 2.4 m³ respectively, its density is

A) 51.0 kg/m³ .
B) 51.4 kg/m³ .
C) 51.39 kg/m³ .
D) 5.14 $\times$ 10 kg/m³ .
E) 5.1 $\times$ 10 kg/m³ .

Question 37

A rectangle is 4.55 m long and 2.3 m wide. The area of the rectangle is

A) 10.46 m².
B) 10.5 m².
C) 10 m².
D) 10.50 m².
E) 10.460 m².

Question 38

A thunderstorm drops 1/4 in. of rain on a 50 mi² area. The estimated number of fallen raindrops is

A) 10¹⁷.
B) 10⁷.
C) 10⁶.
D) 100,000.
E) 10^-6.

Question 39

A student measures the length of an object five times, each time using a different instrument. $\begin{array} { l l l l l l } \text { Measurement } & 1 & 2 & 3 & 4 & 5 \\\text { Length (m) } & 74.14 & 74 & 75 & 74.2 & 73.9\end{array}$ The least precise measurement is

A) 1.
B) 2.
C) 3.
D) 4.
E) 5.

Question 40

The best estimate of the volume of your body is

A) 10³ l.
B) 10² l.
C) 10 l.
D) 10^-1 l.
E) 10^-2 l.

Question 41

A good estimate of the speed of a cliff diver entering the water is

A) 10^-1m/s.
B) 1 m/s.
C) 10 m/s.
D) 10² m/s.
E) 10³ m/s.

Question 42

A good estimate of the number of cars stuck in traffic on a four-lane freeway in one mile is

A) 10.
B) 10³.
C) 10⁵.
D) 10⁷.
E) 10¹⁰.

Question 43

A good estimate of the number of cans of soda needed to fill an Olympic-size swimming pool is

A) 10³.
B) 10⁵.
C) 10⁷.
D) 10⁹.
E) 10¹¹.

Question 44

To estimate the height of a pillar, you walk about 70 steps from the pillar. At this point, the angle made by the line of sight to the top of the pillar with the horizontal is 30^o. The height of the pillar is

A) 10 m.
B) 20 m.
C) 50 m.
D) 80 m.
E) 100 m.

Question 45

The Roosevelt Island Tramway in New York City spans the East River and connects Roosevelt Island to Manhattan. It is the only commuter aerial tramway in North America. Between two particular points, the altitude change is 50 ft when the horizontal distance between them is 100 ft. The grade (the steepness) of this portion of the path is

A) 0.35.
B) 0.50.
C) 1.0.
D) 2.0.
E) 4.0.