Q: You are given a speed of 5 miles per hour (mph). Using the conversion factors $$1 \mathrm{mi} = 5280 \mathrm{ft}$$, $$1 \mathrm{ft} = 12 \mathrm{in}$$, $$1 \mathrm{in} = 2.54 \mathrm{cm}$$, and $$1 \mathrm{m} = 100 \mathrm{cm}$$, what is the correct setup to convert 5 mph to meters per second (m/s)?

$$5 \times \frac{5280 \ \mathrm{ft}}{1 \ \mathrm{mi}} \times \frac{12 \ \mathrm{in}}{1 \ \mathrm{ft}} \times \frac{2.54 \ \mathrm{cm}}{1 \ \mathrm{in}} \times \frac{1 \ \mathrm{m}}{100 \ \mathrm{cm}} \times \frac{1}{3600}$$

Question 1

Which of the following is NOT an SI base unit?

Accepted Answer

inch

Question 2

A scientist uses the formula $$v = A x^2$ t to $$describe the motion of a particle, where $$v is $$velocity, $$x is $$position, and $$t is $$time. What are the SI units of the constant $$A$$?

Accepted Answer

$$\mathrm{m}^{-1} \mathrm{s}^{-1}$$

Question 3

Which of the following countries does NOT primarily use the SI system?

Accepted Answer

United States

Question 4

You are given a speed of 5 miles per hour (mph). Using the conversion factors $$1 \mathrm{mi} = 5280 \mathrm{ft}$$, $$1 \mathrm{ft} = 12 \mathrm{in}$$, $$1 \mathrm{in} = 2.54 \mathrm{cm}$$, and $$1 \mathrm{m} = 100 \mathrm{cm}$$, what is the correct setup to convert 5 mph to meters per second (m/s)?

Accepted Answer

$$5 	imes \frac{5280 \ \mathrm{ft}}{1 \ \mathrm{mi}} 	imes \frac{12 \ \mathrm{in}}{1 \ \mathrm{ft}} 	imes \frac{2.54 \ \mathrm{cm}}{1 \ \mathrm{in}} 	imes \frac{1 \ \mathrm{m}}{100 \ \mathrm{cm}} 	imes \frac{1}{3600}$$

Question 5

Which of the following best describes the purpose of dimensional analysis in physics?

Accepted Answer

To check if the units in an equation are consistent and make sense

Question 6

Given the equation $$v = A x^2$ t + B \frac{x^2$}{t}$$, what are the SI units of $$B$$?

Accepted Answer

$$\mathrm{m}^{-1} \mathrm{s}$$

Question 7

Which of the following is an example of an order of magnitude estimate?

Accepted Answer

Estimating the number of people in a stadium by rounding to the nearest power of ten

Question 8

A student wants to estimate the total volume of trash produced by a university in a year. Which of the following steps is NOT part of a proper order of magnitude estimate?

Accepted Answer

Calculate the answer to six significant figures

Question 9

Which of the following is the correct sequence for the APECR problem-solving method?

Accepted Answer

Assess, Plan, Execute, Check, Reflect

Question 10

If you are converting 10 kilometers to meters using SI units, which conversion factor should you use?

Accepted Answer

$$1 \ \mathrm{km} = 1000 \ \mathrm{m}$$

Question 11

Which of the following is a correct dimensional analysis for checking the units of acceleration ($$a) in $$the equation $$F = m a$$?

Accepted Answer

$$[a] = \frac{[F]}{[m]} = \frac{\mathrm{kg} \cdot \mathrm{m}/\mathrm{s}^2}{\mathrm{kg}} = \mathrm{m}/\mathrm{s}^2$$

Question 12

Which of the following is NOT a base SI unit?

Accepted Answer

liter

Question 13

A physics student is asked to convert 100 inches to meters. Which of the following conversion factors is NOT needed?

Accepted Answer

$$1 \ \mathrm{kg} = 1000 \ \mathrm{g}$$

Question 14

Which of the following best describes a 'back of the envelope' calculation?

Accepted Answer

A rough estimate using approximate values and powers of ten

Question 15

If a formula for energy is given as $$E = C m^2$ t$$^{-3}$$, where E$ is energy, m$ is mass, and t$ is time, what are the SI units of the constant C$?

Accepted Answer

$$\mathrm{kg}^{-1} \mathrm{m}^2 \mathrm{s}^{-3}$$

Question 16

Which of the following is a correct example of using a conversion factor to change 20 centimeters to meters?

Accepted Answer

$$20 	imes \frac{1 \ \mathrm{m}}{100 \ \mathrm{cm}}$$

Chapter 1: Units, Dimensional Analysis, and Order of Magnitude Estimates

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