Q: A car travels 3 km east, then 4 km north. What is the magnitude of its displacement?

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

Q: A plane flies with a velocity of $$500\ \text{km/h}$$ due south. Another plane flies at $$700\ \text{km/h} at$$ $$60^\circ$$ east of south. What is the magnitude of the relative velocity of the second plane with respect to the first?

$$\sqrt{500^2$ + 700^2$ - 2 \times 500 \times 700 \times \cos 60^\circ} = 583\ \text{km/h}$$

Question 1

Which of the following best describes the difference between distance and displacement?

Accepted Answer

Distance is the total length of the path traveled, while displacement is the straight-line change in position from the initial to the final point.

Question 2

A car travels 3 km east, then 4 km north. What is the magnitude of its displacement?

Accepted Answer

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

Question 3

If a vector $$\vec{A}$$ has components $$A_x = 6$$ and $$A_y = 8$$, what is the magnitude of $$\vec{A}$$?

Accepted Answer

$$\sqrt{6^2$ + 8^2$} = 10$$

Question 4

Which of the following is a scalar quantity?

Accepted Answer

Temperature

Question 5

A plane flies with a velocity of $$500\ 	ext{km/h}$$ due south. Another plane flies at $$700\ 	ext{km/h} at$$ $$60^\circ$$ east of south. What is the magnitude of the relative velocity of the second plane with respect to the first?

Accepted Answer

$$\sqrt{500^2$ + 700^2$ - 2 	imes 500 	imes 700 	imes \cos 60^\circ} = 583\ 	ext{km/h}$$

Question 6

If each component of a vector is doubled, what happens to the angle of that vector?

Accepted Answer

It does not change.

Question 7

Given $$\vec{A} + \vec{B} = 0$$, what can you say about the magnitude and direction of $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

They have the same magnitude but must be in opposite directions.

Question 8

A child pushes a box to the right with a force of $$10\ 	ext{N}$$, then pulls it to the left with a force of $$10\ 	ext{N}. $$What is the net force on the box?

Accepted Answer

$$0\ 	ext{N}$$

Question 9

Which of the following statements about displacement is correct?

Accepted Answer

Displacement depends only on the initial and final positions, not on the path taken.

Question 10

Given $$\vec{D} = 6\hat{i} + 3\hat{j} - 1\hat{k}$$ and $$\vec{E} = 4\hat{i} - 5\hat{j} + 8\hat{k}$$, what is the magnitude of $$2\vec{D} - \vec{E}$$?

Accepted Answer

$$\sqrt{8^2$ + 11^2$ + (-10)^2$} = \sqrt{285} \approx 16.9$$

Question 11

If $$\vec{A} + \vec{B} = \vec{C}$$ and $$|\vec{A}| + |\vec{B}| = |\vec{C}|$$, how are $$\vec{A}$$ and $$\vec{B}$$ oriented with respect to each other?

Accepted Answer

They are parallel and in the same direction.

Question 12

A ball is thrown straight up and returns to its initial position. During the time the ball is in the air, which of the following is true?

Accepted Answer

Average velocity is zero but average acceleration is not zero.

Question 13

Which of the following is true about the speedometer in a car?

Accepted Answer

It measures speed, which is a scalar quantity.

Question 14

A skydiver falls straight down (negative $$y$$ direction). Her speed increases from $$16\ 	ext{m/s} to$$ $$28\ 	ext{m/s} in$$ $$1.5\ 	ext{s}. $$Which of the following is correct?

Accepted Answer

$$v  0$$

Question 15

If a vector $$\vec{A} is $$multiplied by a negative scalar, what happens to its direction and magnitude?

Accepted Answer

The magnitude is scaled and the direction is reversed.

Question 16

A car is traveling with an initial velocity $$v_0. At$$ $$t = 0$$, the driver applies the brakes, causing a constant acceleration $$-a_b. At $$what time $$t_f$$ does the car stop?

Accepted Answer

$$t_f = \frac{v_0$}{a_b}$$

Question 17

Which of the following is the correct formula for the $$x-$$component of a vector $$\vec{A} at an $$angle $$	heta$$ from the $$x-$$axis?

Accepted Answer

$$A_x = A \cos 	heta$$

Question 18

A kingfisher dives from a height of $$7.0\ 	ext{m}$$ with an average speed of $$4.00\ 	ext{m/s}. $$How long does it take to reach the water?

Accepted Answer

$$t = \frac{7.0}{4.00} = 1.75\ 	ext{s}$$

Vectors and Motion in One Dimension: Foundations of Physics with Calculus

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