Q: A runner jogs 400 m east, then 300 m north. What is the direction of the net displacement vector relative to east?

$$\theta = \tan$$^{-1}$$\left(\frac{300}{400}\right) = 37$$^{\circ}$$ north of east$

Q: A cyclist rides 5 km west in 0.5 hours. What is her average velocity?

$$v = \frac{\Delta x}{\Delta t} = \frac{-5\ \text{km}}{0.5\ \text{h}} = -10\ \text{km/h}$$

Q: A car moves at a constant speed of 20 m/s for 15 seconds. How far does it travel?

$$d = v t = 20 \times 15 = 300 m$

Q: A student estimates their walking speed as 1 m/s. If they walk 2 km to campus, how long does it take in minutes?

$$t = \frac{2000\ \text{m}}{1\ \text{m/s}} = 2000\ \text{s} = 33.3\ \text{min}$$

Question 1

A car travels 120 km east in 2 hours, then 150 km north in 3 hours. What is the magnitude of the car's net displacement from its starting point?

Accepted Answer

$$\sqrt{(120^2$ + 150^2$)} = 192 km$

Question 2

Which of the following statements best describes the difference between speed and velocity?

Accepted Answer

Velocity contains information about the direction of motion while speed does not.

Question 3

A runner jogs 400 m east, then 300 m north. What is the direction of the net displacement vector relative to east?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{300}{400}ight) = 37$$^{\circ}$$ north of east$

Question 4

A cyclist rides 5 km west in 0.5 hours. What is her average velocity?

Accepted Answer

$$v = \frac{\Delta x}{\Delta t} = \frac{-5\ 	ext{km}}{0.5\ 	ext{h}} = -10\ 	ext{km/h}$$

Question 5

Which of the following is a vector quantity?

Accepted Answer

Displacement

Question 6

A ball is thrown at a $$60^{\circ}$$ angle above the horizontal. Which statement about its velocity vector at the highest point is correct?

Accepted Answer

The velocity vector is horizontal and points in the direction of motion.

Question 7

A measurement is recorded as 0.0520 m. How many significant figures does this value have?

Accepted Answer

3

Question 8

Which of the following is the correct SI unit for mass?

Accepted Answer

Kilogram (kg)

Question 9

A person walks 100 m east, then 200 m west. What is the magnitude of their net displacement?

Accepted Answer

$$|100 - 200| = 100 m$

Question 10

A car moves at a constant speed of 20 m/s for 15 seconds. How far does it travel?

Accepted Answer

$$d = v t = 20 	imes 15 = 300 m$

Question 11

Which of the following best describes the particle model in physics?

Accepted Answer

It treats a moving object as if all its mass were concentrated at a single point.

Question 12

A student estimates their walking speed as 1 m/s. If they walk 2 km to campus, how long does it take in minutes?

Accepted Answer

$$t = \frac{2000\ 	ext{m}}{1\ 	ext{m/s}} = 2000\ 	ext{s} = 33.3\ 	ext{min}$$

Question 13

Which of the following is an order-of-magnitude estimate for the number of seconds in a day?

Accepted Answer

$$10^5$$

Question 14

A vector has components $$3$$ units east and $$4$$ units north. What is its magnitude?

Accepted Answer

$$\sqrt{3^2$ + 4^2$} = 5$$ units$

Question 15

A goose flies 21 miles north, then 28 miles east. What is the straight-line distance from its starting point to its final position?

Accepted Answer

$$\sqrt{21^2$ + 28^2$} = 35$$ miles$

Question 16

Which of the following is a correct rule for significant figures in multiplication?

Accepted Answer

The answer should have the same number of significant figures as the value with the fewest significant figures.

Question 17

A car's velocity changes from 30 m/s east to 10 m/s east in 5 seconds. What is the average acceleration?

Accepted Answer

$$a = \frac{10 - 30}{5} = -4 m/s$^2$$

Question 18

Which of the following is NOT a scalar quantity?

Accepted Answer

Velocity

Question 19

A measurement is recorded as $$6.370000 	imes 10^6$ m. How many significant figures does this value have?

Accepted Answer

7

Question 20

A student converts 60 miles to kilometers using the conversion factor $$1\ 	ext{mi} = 1.609\ 	ext{km}. $$What is the result, rounded to two significant figures?

Accepted Answer

$$60 	imes 1.609 = 97 km$

Chapter 1: Representing Motion – Physics with Calculus Study Notes

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