Q: A standard sheet of paper measures 8.5 inches by 11.0 inches. What is the area of the paper in $$\mathrm{cm}^2$$? (Use $$1\ \mathrm{in} = 2.54\ \mathrm{cm})$$

$$8.5 \times 11.0 \times (2.54)^2$ = 237.9\ \mathrm{cm}^2$$

Q: How many cubic inches are in a box with a volume of $$1.0\ \mathrm{m}^3$$? (Use $$1\ \mathrm{in} = 2.54\ \mathrm{cm})$$

$$1.0\ \mathrm{m}^3 \times \left(\dfrac{100\ \mathrm{cm}}{1\ \mathrm{m}}\$$right)^3$$ \times \left(\dfrac{1\ \mathrm{in}}{2.54\ \mathrm{cm}}\$$right)^3$$ = 61,023.74\ \mathrm{in}^3$$

Q: If a box has a volume of $$1.0\ \mathrm{m}^3$$, what is its volume in $$\mathrm{cm}^3$$?

$$1.0\ \mathrm{m}^3 \times (100\ \mathrm{cm}/1\ \mathrm{m})^3$ = 1,000,000\ \mathrm{cm}^3$$

Question 1

A standard sheet of paper measures 8.5 inches by 11.0 inches. What is the area of the paper in $$\mathrm{cm}^2$$? (Use $$1\ \mathrm{in} = 2.54\ \mathrm{cm})$$

Accepted Answer

$$8.5 	imes 11.0 	imes (2.54)^2$ = 237.9\ \mathrm{cm}^2$$

Question 2

How many cubic inches are in a box with a volume of $$1.0\ \mathrm{m}^3$$? (Use $$1\ \mathrm{in} = 2.54\ \mathrm{cm})$$

Accepted Answer

$$1.0\ \mathrm{m}^3 	imes \left(\dfrac{100\ \mathrm{cm}}{1\ \mathrm{m}}\$$right)^3$$ 	imes \left(\dfrac{1\ \mathrm{in}}{2.54\ \mathrm{cm}}\$$right)^3$$ = 61,023.74\ \mathrm{in}^3$$

Question 3

Which of the following best explains why motion is considered relative?

Accepted Answer

Because the observed motion of an object depends on the observer's frame of reference.

Question 4

A pedestrian stands on the sidewalk as a blue car passes by. From the pedestrian's perspective, how is the motion of the front seat passenger in the blue car described?

Accepted Answer

The front seat passenger is moving forward with the same velocity as the blue car.

Question 5

If you are sitting in the back seat of a blue car moving east, and you see a green car directly behind you moving faster in the same direction, how does the green car's motion appear to you?

Accepted Answer

The green car appears to be approaching from behind, moving east faster than your car.

Question 6

A red car is passing a blue car, both moving in the same direction. From the perspective of the driver of the red car, how does the blue car appear to move?

Accepted Answer

The blue car appears to be moving backward relative to the red car.

Question 7

Which of the following is a correct multi-step process for converting $$1.0\ \mathrm{m}^3 to$$ $$\mathrm{in}^3$$?

Accepted Answer

First convert $$\mathrm{m}^3 to$$ $$\mathrm{cm}^3$$, then convert $$\mathrm{cm}^3 to$$ $$\mathrm{in}^3$$ using $$1\ \mathrm{in} = 2.54\ \mathrm{cm}.$$

Question 8

In a train moving east, Ryan walks toward the rear of the train. From the perspective of a stationary observer outside the train, what is Ryan's direction of motion?

Accepted Answer

Ryan is moving east, but at a slower speed than the train.

Question 9

Which assumption is necessary when providing directions using a map?

Accepted Answer

The person receiving directions understands the map legend and scale.

Question 10

If a box has a volume of $$1.0\ \mathrm{m}^3$$, what is its volume in $$\mathrm{cm}^3$$?

Accepted Answer

$$1.0\ \mathrm{m}^3 	imes (100\ \mathrm{cm}/1\ \mathrm{m})^3$ = 1,000,000\ \mathrm{cm}^3$$

Question 11

Which statement best describes the role of a reference object in describing motion?

Accepted Answer

A reference object provides a fixed point to compare the position and motion of other objects.

Question 12

A dot diagram shows dots spaced equally apart. What does this indicate about the object's motion?

Accepted Answer

The object is moving at a constant speed (uniform motion).

Question 13

If you are a passenger in a car moving east and you see another car moving west, what is the relative velocity of the other car with respect to you?

Accepted Answer

The relative velocity is the sum of the speeds of both cars, directed west.

Question 14

Why is it important to use the correct conversion factor when converting units of area or volume?

Accepted Answer

Because area and volume conversions require squaring or cubing the linear conversion factor.

Question 15

A map legend helps you give directions by:

Accepted Answer

Explaining the meaning of symbols and scales on the map.

Question 16

If Ryan walks toward the rear of a train moving east, and Jan says Ryan is moving west, which concept explains the disagreement?

Accepted Answer

Motion is relative to the observer's frame of reference.

Question 17

Which of the following is NOT a plausible assumption when giving directions using a map?

Accepted Answer

The person can teleport instantly to any location.

Question 18

If a dot diagram shows dots getting closer together over time, what does this indicate about the object's motion?

Accepted Answer

The object is slowing down (decelerating).

Question 19

When converting $$\mathrm{m}^3 to$$ $$\mathrm{in}^3$$, which exponent should be applied to the conversion factor $$1\ \mathrm{in} = 2.54\ \mathrm{cm}$$?

Accepted Answer

Exponent 3, because volume is a cubic measurement.

Area and Volume Conversions; The Concept of Relative Motion

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