Q: The position $$x of an $$object is given by $$x = A + Bt + Ct^2$, where t$ is time in seconds. What are the SI units of A$, B$, and C$?

$$\text{m},~\text{m/s},~\text{m/s}^2$$

Q: A weight lifter can bench press $$171~\text{kg}. $$How many milligrams (mg) is this?

$$1.71 \times 10^8$~\text{mg}$$

Q: The shortest wavelength of visible light is approximately $$400~\text{nm}. $$Express this wavelength in centimeters.

$$4 \times 10$$^{-5}$$~\text{cm}$$

Q: A plot of land contains $$7.1~\text{hectares}. $$How many square meters does it contain? (1 hectare = $$10^4$$~\text{m}^2$$)

$$7.1 \times 10^4$~\text{m}^2$$

Q: A person on a diet loses $$1.6~\text{kg} in a $$week. How many micrograms per second ($$\mu\text{g}/\text{s}) $$are lost? (1 week = 604800 s, 1 kg = $$10^9$$~\mu\text{g}$$)

$$2.6 \times 10^3$~\mu\text{g}/\text{s}$$

Question 1

The current definition of the standard meter is based on which physical principle?

Accepted Answer

The distance traveled by light in a vacuum.

Question 2

A woman weighs 125 lb. What is her mass in kilograms, given that $$1~	ext{lb} = 0.4536~	ext{kg}$$? Is her mass in kg less than or greater than 125?

Accepted Answer

Her mass in kg is less than 125.

Question 3

Convert $$15~	ext{m} to $$feet, given $$1~	ext{m} = 3.281~	ext{ft}. Is $$the height in feet less than or greater than 15?

Accepted Answer

The height in feet is greater than 15.

Question 4

When adding two numbers, the number of significant figures in the sum is determined by:

Accepted Answer

The least accurate decimal place among the numbers being added.

Question 5

Express $$1.2 	imes 10$$^{-3}$$ in decimal notation.

Accepted Answer

0.0012

Question 6

How many significant figures are in the number $$0.003010$$?

Accepted Answer

4 significant figures

Question 7

A computer screen has an area of $$1.27~	ext{ft}^2. $$Convert this area to $$	ext{m}^2$$ using $$1~	ext{ft} = 0.3048~	ext{m}. $$What is the closest value?

Accepted Answer

0.118~	ext{m}^2

Question 8

A marathon is 26 miles and 385 yards long. If the average stride is $$5~	ext{ft}$$, estimate the number of strides required to run a marathon. (1 mile = 5280 ft, 1 yard = 3 ft)

Accepted Answer

$$4.5 	imes 10^4$ strides

Question 9

The period $$T of a $$pendulum depends only on the acceleration due to gravity $$g$$ and the length $$\ell. $$Which combination of $$g$$ and $$\ell$$ gives the correct proportionality for $$T$$?

Accepted Answer

$$\sqrt{\ell / g}$$

Question 10

The speed $$v of a $$wave pulse on a string depends on the tension $$F$$ and mass per unit length $$\mu. $$Which combination gives the correct proportionality for $$v$$?

Accepted Answer

$$\sqrt{F / \mu}$$

Question 11

The position $$x of an $$object is given by $$x = A + Bt + Ct^2$, where t$ is time in seconds. What are the SI units of A$, B$, and C$?

Accepted Answer

$$	ext{m},~	ext{m/s},~	ext{m/s}^2$$

Question 12

A weight lifter can bench press $$171~	ext{kg}. $$How many milligrams (mg) is this?

Accepted Answer

$$1.71 	imes 10^8$~	ext{mg}$$

Question 13

The shortest wavelength of visible light is approximately $$400~	ext{nm}. $$Express this wavelength in centimeters.

Accepted Answer

$$4 	imes 10$$^{-5}$$~	ext{cm}$$

Question 14

A computer performs $$6.7 	imes 10^7$ calculations per second. How many nanoseconds does it take to perform one calculation?

Accepted Answer

15 ns

Question 15

Estimate the number of times the average human heart beats in a year, assuming a heart rate of 70 beats per minute.

Accepted Answer

$$4 	imes 10^6$

Question 16

Express $$(4.3 	imes 10^6$)^{-1/2}$ in scientific notation.

Accepted Answer

$$2.1 	imes 10$$^{-4}$$

Question 17

A plot of land contains $$7.1~	ext{hectares}. $$How many square meters does it contain? (1 hectare = $$10^4$$~	ext{m}^2$$)

Accepted Answer

$$7.1 	imes 10^4$~	ext{m}^2$$

Question 18

A person on a diet loses $$1.6~	ext{kg} in a $$week. How many micrograms per second ($$\mu	ext{g}/	ext{s}) $$are lost? (1 week = 604800 s, 1 kg = $$10^9$$~\mu	ext{g}$$)

Accepted Answer

$$2.6 	imes 10^3$~\mu	ext{g}/	ext{s}$$

Physics with Calculus: Units, Conversions, and Estimation – Step-by-Step Guidance

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