Q: A car is moving at a speed of 150 km/h. What is this speed in meters per second ($$\text{m/s}$$)?

$$150 \times \frac{1000}{3600} = 41.7\ \text{m/s}$$

Q: The universe is thought to be about 13.7 billion years old. What is its age in seconds? (1 year = $$3.15 \times 10^7$ s)

$$13.7 \times 10^9$ \times 3.15 \times 10^7$ = 4.32 \times 10$$^{17}$$\ \text{s}$$

Q: Our species evolved about $$4.7 \times 10$$^{12}$$ seconds ago. How many years is that? (1 year = 3.15$$ \times $$10^7 s)$$

$$\frac{4.7 \times 10$$^{12}$$}{3.15 \times 10^7$} = 1.49 \times 10^5$\ \text{years}$$

Q: Calculate the value of energy $$E$$ for an electron using $$E = mc^2$, where m = 9.11$$ \times $$10^{-31}$$\ \text{kg}$$ and c = 3.00$$ \times $$10^8$$\ \text{m/s}$$. Express your answer with three significant figures.

$$E = 9.11 \times 10$$^{-31}$$ \times (3.00 \times 10^8$)^2 = 8.20$$ \times $$10^{-14}$$\ \text{J}$

Q: Evaluate $$\frac{0.132}{0.0492 \times 0.56} to $$the correct number of significant figures.

$$\frac{0.132}{0.0492 \times 0.56} = 4.8$$

Q: You travel 2.00 km north and then 5.00 km west. What is the magnitude of your resultant displacement?

$$\sqrt{(2.00)^2$ + (5.00)^2$} = 5.39\ \text{km}$$

Q: You travel 2.00 km north and then 5.00 km west. What is the direction of your resultant displacement relative to west?

$$\theta = \tan$$^{-1}$$\left(\frac{2.00}{5.00}\right) = 21.8^\circ$$ north of west

Q: A dog walks straight east and then straight north, ending up 600 m from the house at $$25^\circ$$ north of east. How far did the dog walk east?

$$600 \cos 25^\circ = 543\ \text{m}$$

Q: A dog walks straight east and then straight north, ending up 600 m from the house at $$25^\circ$$ north of east. How far did the dog walk north?

$$600 \sin 25^\circ = 254\ \text{m}$$

Q: A cat walks first straight west and then straight south, ending up 800 m from the starting point at $$65^\circ$$ south of west. How far did the cat walk west?

$$800 \cos 65^\circ = 338\ \text{m}$$

Question 1

A car is moving at a speed of 150 km/h. What is this speed in meters per second ($$	ext{m/s}$$)?

Accepted Answer

$$150 	imes \frac{1000}{3600} = 41.7\ 	ext{m/s}$$

Question 2

The universe is thought to be about 13.7 billion years old. What is its age in seconds? (1 year = $$3.15 	imes 10^7$ s)

Accepted Answer

$$13.7 	imes 10^9$ 	imes 3.15 	imes 10^7$ = 4.32 	imes 10$$^{17}$$\ 	ext{s}$$

Question 3

Our species evolved about $$4.7 	imes 10$$^{12}$$ seconds ago. How many years is that? (1 year = 3.15$$ 	imes $$10^7 s)$$

Accepted Answer

$$\frac{4.7 	imes 10$$^{12}$$}{3.15 	imes 10^7$} = 1.49 	imes 10^5$\ 	ext{years}$$

Question 4

Given the equation $$F = bV^2$, where F$ is force in $$	ext{kg}\cdot	ext{m}/	ext{s}^2$$ and V$ is speed in $$	ext{m}/	ext{s}$$, what are the SI units of b$ for dimensional consistency?

Accepted Answer

Question 5

Calculate the value of energy $$E$$ for an electron using $$E = mc^2$, where m = 9.11$$ 	imes $$10^{-31}$$\ 	ext{kg}$$ and c = 3.00$$ 	imes $$10^8$$\ 	ext{m/s}$$. Express your answer with three significant figures.

Accepted Answer

$$E = 9.11 	imes 10$$^{-31}$$ 	imes (3.00 	imes 10^8$)^2 = 8.20$$ 	imes $$10^{-14}$$\ 	ext{J}$

Question 6

Evaluate $$\frac{0.132}{0.0492 	imes 0.56} to $$the correct number of significant figures.

Accepted Answer

$$\frac{0.132}{0.0492 	imes 0.56} = 4.8$$

Question 7

You travel 2.00 km north and then 5.00 km west. What is the magnitude of your resultant displacement?

Accepted Answer

$$\sqrt{(2.00)^2$ + (5.00)^2$} = 5.39\ 	ext{km}$$

Question 8

You travel 2.00 km north and then 5.00 km west. What is the direction of your resultant displacement relative to west?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{2.00}{5.00}ight) = 21.8^\circ$$ north of west

Question 9

A dog walks straight east and then straight north, ending up 600 m from the house at $$25^\circ$$ north of east. How far did the dog walk east?

Accepted Answer

$$600 \cos 25^\circ = 543\ 	ext{m}$$

Question 10

A dog walks straight east and then straight north, ending up 600 m from the house at $$25^\circ$$ north of east. How far did the dog walk north?

Accepted Answer

$$600 \sin 25^\circ = 254\ 	ext{m}$$

Question 11

A cat walks first straight west and then straight south, ending up 800 m from the starting point at $$65^\circ$$ south of west. How far did the cat walk west?

Accepted Answer

$$800 \cos 65^\circ = 338\ 	ext{m}$$

Question 12

A cat walks first straight west and then straight south, ending up 800 m from the starting point at $$65^\circ$$ south of west. How far did the cat walk south?

Accepted Answer

$$800 \sin 65^\circ = 725\ 	ext{m}$$

Question 13

Vector A has a magnitude of 60 cm at $$40^\circ$$, and vector B has a magnitude of 45 cm at $$120^\circ ($$angles measured counterclockwise from the positive x-axis). What is the x-component of the vector sum?

Accepted Answer

$$60 \cos 40^\circ + 45 \cos 120^\circ = 45.96 - 22.5 = 23.46\ 	ext{cm}$$

Question 14

Vector A has a magnitude of 60 cm at $$40^\circ$$, and vector B has a magnitude of 45 cm at $$120^\circ. $$What is the y-component of the vector sum?

Accepted Answer

$$60 \sin 40^\circ + 45 \sin 120^\circ = 38.57 + 38.96 = 77.53\ 	ext{cm}$$

Question 15

Vector A has a magnitude of 60 cm at $$40^\circ$$, and vector B has a magnitude of 45 cm at $$120^\circ. $$What is the magnitude of the vector sum?

Accepted Answer

$$\sqrt{(23.46)^2$ + (77.53)^2$} = 80.0\ 	ext{cm}$$

Question 16

Four students receive three displacements: $$52.0 m at$$ $$30.0^\circ$$ east of north, $$41.0 m at$$ $$45.0^\circ$$ south of east, and $$35.0 m $$west. What is the x-component of the total displacement?

Accepted Answer

$$52.0 \sin 30.0^\circ + 41.0 \cos 45.0^\circ - 35.0 = 26.0 + 29.0 - 35.0 = 20.0\ 	ext{m}$$

Question 17

Four students receive three displacements: $$52.0 m at$$ $$30.0^\circ$$ east of north, $$41.0 m at$$ $$45.0^\circ$$ south of east, and $$35.0 m $$west. What is the y-component of the total displacement?

Accepted Answer

$$52.0 \cos 30.0^\circ - 41.0 \sin 45.0^\circ = 45.0 - 29.0 = 16.0\ 	ext{m}$$

Question 18

Four students receive three displacements: $$52.0 m at$$ $$30.0^\circ$$ east of north, $$41.0 m at$$ $$45.0^\circ$$ south of east, and $$35.0 m $$west. What is the magnitude of the total displacement?

Accepted Answer

$$\sqrt{(20.0)^2$ + (16.0)^2$} = 25.6\ 	ext{m}$$

Physics with Calculus: Chapter 1 Study Guidance (Units, Vectors, Significant Figures)

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