Q: A car travels at 55 mi/h. What is its speed in SI units (m/s)? Use the conversion factors: $$1.609 \ \text{km} = 1 \ \text{mi}$$ and $$1000 \ \text{m} = 1 \ \text{km}.$$

$$55 \ \text{mi/h} \times \frac{1.609 \ \text{km}}{1 \ \text{mi}} \times \frac{1000 \ \text{m}}{1 \ \text{km}} \times \frac{1 \ \text{h}}{3600 \ \text{s}} = 25.4 \ \text{m/s}$$

Q: Which of the following is the correct definition of the dot (scalar) product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

$$\vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos \theta$$

Question 1

Which of the following is the correct SI base unit for mass, and what is unique about its prefix compared to other SI base units?

Accepted Answer

The kilogram (kg); it is the only SI base unit with a prefix.

Question 2

A car travels at 55 mi/h. What is its speed in SI units (m/s)? Use the conversion factors: $$1.609 \ 	ext{km} = 1 \ 	ext{mi}$$ and $$1000 \ 	ext{m} = 1 \ 	ext{km}.$$

Accepted Answer

$$55 \ 	ext{mi/h} 	imes \frac{1.609 \ 	ext{km}}{1 \ 	ext{mi}} 	imes \frac{1000 \ 	ext{m}}{1 \ 	ext{km}} 	imes \frac{1 \ 	ext{h}}{3600 \ 	ext{s}} = 25.4 \ 	ext{m/s}$$

Question 3

Which of the following statements about adding physical quantities is correct?

Accepted Answer

You can only add two quantities if they have the same units.

Question 4

A steel rod is measured to have a diameter of $$56.47 \ 	ext{mm} \pm 0.02 \ 	ext{mm}. $$What is the fractional uncertainty in this measurement?

Accepted Answer

$$\frac{0.02}{56.47} = 0.0004$$

Question 5

Which of the following numbers has three significant figures?

Accepted Answer

0.00250

Question 6

When multiplying or dividing measured quantities, how many significant figures should the result have?

Accepted Answer

The result should have no more significant figures than the factor with the fewest significant figures.

Question 7

A vector $$\vec{A}$$ has a magnitude of $$5$$ and points $$30^\circ$$ above the negative x-axis. What are its x and y components?

Accepted Answer

$$A_x = -5 \cos 30^\circ$$, $$A_y = 5 \sin 30^\circ$$

Question 8

Which of the following best describes a scalar quantity?

Accepted Answer

A physical quantity that has magnitude but no direction.

Question 9

If a vector $$\vec{A}$$ has components $$A_x = -3$$ and $$A_y = 4$$, what is its magnitude and direction (measured counterclockwise from the +x-axis)?

Accepted Answer

Magnitude: $$5$$, Direction: $$126.87^\circ$$

Question 10

Which of the following is the correct definition of the dot (scalar) product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$\vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos 	heta$$

Question 11

Given $$\vec{A} = 3\hat{i} + 4\hat{j}$$ and $$\vec{B} = -8\hat{i} + 6\hat{j}$$, what is $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

$$14$$

Question 12

A displacement vector points $$60^\circ$$ above the +x-axis and has a magnitude of $$10 m. $$What are its x and y components?

Accepted Answer

$$A_x = 10 \cos 60^\circ$$, \ A_y = 10 \sin 60^\circ$

Question 13

If two vectors $$\vec{A}$$ and $$\vec{B}$$ are perpendicular, what is their dot product?

Accepted Answer

$$0$$

Question 14

A resistor is labeled $$47 \ \Omega \pm 10\%. $$What is the possible range of its true resistance?

Accepted Answer

$$42.3 \ \Omega to$$ $$51.7 \ \Omega$$

Question 15

Which of the following best describes the process of converting units for a quantity raised to a power (e.g., area or volume)?

Accepted Answer

Raise the conversion factor to the same power as the quantity.

Question 16

Which of the following is a correct statement about the magnitude of a vector and its components?

Accepted Answer

The magnitude of a vector is always positive or zero, but its components can be positive, negative, or zero.

Question 17

If $$\vec{A} = 4\hat{i} + 7\hat{j}$$ and $$\vec{B} = 5\hat{i} - 2\hat{j}$$, what is the angle $$	heta$$ between $$\vec{A}$$ and $$\vec{B}$$? (Use $$\vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos 	heta.)$$

Accepted Answer

$$	heta = 42.2^\circ$$

Question 18

Which of the following is NOT a correct property of vectors?

Accepted Answer

The sum of the magnitudes of two vectors is always equal to the magnitude of their sum.

Physical Quantities, Units, and Measurement in Physics

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