Q: Which of the following equations correctly converts from polar to rectangular coordinates for a point $$(r, \theta)$$?

$$x = r \cos \theta$$, $$y = r \sin \theta$$

Q: A distance is measured as $$5.2 cm. $$Express this value in meters using scientific notation.

$$5.2 \times 10$$^{-2}$$\ \mathrm{m}$$

Question 1

Which of the following best describes the object shown in the first image (the glass-encased cylinder) and its significance in physics?

Accepted Answer

It is the International Prototype of the Kilogram, which was used as the standard for mass in the SI system.

Question 2

The second image shows a modern device used to define the SI unit of time. What physical phenomenon does this device rely on?

Accepted Answer

The oscillation of radiation from a cesium atom.

Question 3

In the Cartesian coordinate system shown in the third image, what are the coordinates of point Q?

Accepted Answer

$$(-3, 4)$$

Question 4

Which of the following equations correctly converts from polar to rectangular coordinates for a point $$(r, 	heta)$$?

Accepted Answer

$$x = r \cos 	heta$$, $$y = r \sin 	heta$$

Question 5

According to the table of metric prefixes, what is the prefix and abbreviation for $$10^{-6}$$?

Accepted Answer

micro, $$\mu$$

Question 6

Which trigonometric function is defined as the ratio of the opposite side to the adjacent side in a right triangle?

Accepted Answer

$$	an 	heta$$

Question 7

Given a right triangle with sides $$x$$ and $$y$$, and hypotenuse $$r$$, which equation is correct according to the Pythagorean theorem?

Accepted Answer

$$r^2$$ = $$x^2$$ + $$y^2$$

Question 8

A person stands 46.0 m from a building and shines a flashlight at an angle of $$39.0^\circ$$ above the horizontal. If the flashlight is held 2.00 m above the ground, what is the total height of the building? (Use $$	an 39.0^\circ = 0.810)$$

Accepted Answer

$$39.3\ \mathrm{m}$$

Question 9

If a speed is given as $$90\ \mathrm{km/h}$$, what is this speed in $$\mathrm{m/s}$$? (1 km = 1000 m, 1 h = 3600 s)

Accepted Answer

$$25\ \mathrm{m/s}$$

Question 10

Which of the following statements about significant figures is correct?

Accepted Answer

When multiplying or dividing, the result should have as many significant figures as the factor with the fewest significant figures.

Question 11

Which of the following is the correct scientific notation for the number 12,150,000,000?

Accepted Answer

$$1.215 	imes 10$$^{10}$$

Question 12

A measurement is recorded as $$0.00450 m. $$How many significant figures does this value have?

Accepted Answer

3

Question 13

Which of the following is NOT a fundamental SI unit?

Accepted Answer

Joule (J)

Question 14

If a calculation yields a result of $$3.14159265$$ and the least accurate measurement has 3 significant figures, how should the result be reported?

Accepted Answer

$$3.14$$

Question 15

Which of the following is the correct dimensional analysis for checking if the equation $$v = d/t is $$dimensionally consistent, where $$v is $$velocity, $$d is $$distance, and $$t is $$time?

Accepted Answer

$$[L][T]^{-1} = [L][T]^{-1}$$

Question 16

A distance is measured as $$5.2 cm. $$Express this value in meters using scientific notation.

Accepted Answer

$$5.2 	imes 10$$^{-2}$$\ \mathrm{m}$$

Question 17

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

Accepted Answer

Approximating the population of a city as $$10^6$$ people.

Question 18

If a building is measured using the method shown in the last image, and the horizontal distance is doubled while keeping the angle the same, what happens to the calculated height difference $$\Delta y ($$ignoring the height of the flashlight)?

Accepted Answer

It doubles.

Question 19

Which of the following best describes the purpose of using models in physics?

Accepted Answer

To simplify complex systems and make predictions that can be tested by experiments.

Chapter 1: Representing Motion – Foundations of Measurement and Mathematical Tools in Physics

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