Q: If the initial position of an object is $$\vec{r}_{\text{ini}}$$ and the final position is $$\vec{r}_{\text{fin}}$$, what is the displacement $$\Delta \vec{r}$$?

$$\Delta \vec{r} = \vec{r}_{\text{fin}} - \vec{r}_{\text{ini}}$$

Q: A car moves from position $$\vec{r}_1 = (2, 3) m to$$ $$\vec{r}_2 = (5, 7) m in 2 $$seconds. What is its average velocity vector?

$$\vec{v}_{\text{avg}} = \left( \frac{3}{2}, \frac{4}{2} \right) = (1.5, 2) m/s$$

Q: Which equation correctly defines average velocity $$\vec{v}_{\text{avg}}$$?

$$\vec{v}_{\text{avg}} = \frac{\Delta \vec{r}}{\Delta t}$$

Q: Which operation is used to find the change in position of an object?

Vector subtraction: $$\Delta \vec{r} = \vec{r}_{\text{fin}} - \vec{r}_{\text{ini}}$$

Question 1

Which of the following correctly describes the result of multiplying a vector $$\vec{A} by a $$scalar $$c$$?

Accepted Answer

The magnitude of $$\vec{A} is $$scaled by $$c$$, and its direction remains unchanged unless $$c is $$negative.

Question 2

Given vectors $$\vec{A}$$ and $$\vec{B}$$, how is the vector $$\vec{C} = \vec{A} - \vec{B}$$ constructed geometrically?

Accepted Answer

$$\vec{C}$$ points from the tip of $$\vec{B} to $$the tip of $$\vec{A}.$$

Question 3

If the initial position of an object is $$\vec{r}_{	ext{ini}}$$ and the final position is $$\vec{r}_{	ext{fin}}$$, what is the displacement $$\Delta \vec{r}$$?

Accepted Answer

$$\Delta \vec{r} = \vec{r}_{	ext{fin}} - \vec{r}_{	ext{ini}}$$

Question 4

A car moves from position $$\vec{r}_1 = (2, 3) m to$$ $$\vec{r}_2 = (5, 7) m in 2 $$seconds. What is its average velocity vector?

Accepted Answer

$$\vec{v}_{	ext{avg}} = \left( \frac{3}{2}, \frac{4}{2} ight) = (1.5, 2) m/s$$

Question 5

Which equation correctly defines average velocity $$\vec{v}_{	ext{avg}}$$?

Accepted Answer

$$\vec{v}_{	ext{avg}} = \frac{\Delta \vec{r}}{\Delta t}$$

Question 6

If a vector $$\vec{A} is $$multiplied by $$-2$$, what happens to its magnitude and direction?

Accepted Answer

The magnitude is doubled and the direction is reversed.

Question 7

A runner starts at $$\vec{r}_{	ext{ini}} = (0,0) m $$and finishes at $$\vec{r}_{	ext{fin}} = (6,8) m in 4 $$seconds. What is the magnitude of the average velocity?

Accepted Answer

$$2.5 m/s$$

Question 8

Which of the following statements about displacement is correct?

Accepted Answer

Displacement is a vector quantity representing the change in position.

Question 9

A cyclist moves from $$\vec{r}_A = (1,2) m to$$ $$\vec{r}_B = (4,6) m in 3 $$seconds. What is the displacement vector?

Accepted Answer

$$(3,4) m$$

Question 10

If $$\vec{A} = (2, 5)$$ and $$\vec{B} = (1, 3)$$, what is $$\vec{A} - \vec{B}$$?

Accepted Answer

$$(1, 2)$$

Question 11

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

Accepted Answer

Displacement is a vector and can be zero even if distance is not.

Question 12

A hiker walks 3 km east and then 4 km north. What is the magnitude of her displacement?

Accepted Answer

$$5 km$$

Question 13

If $$\vec{v}_{	ext{avg}} = \frac{\Delta \vec{r}}{\Delta t}$$, what is the average velocity for $$\Delta \vec{r} = (6, 8) m $$and $$\Delta t = 2 s$$?

Accepted Answer

$$(3, 4) m/s$$

Question 14

Which operation is used to find the change in position of an object?

Accepted Answer

Vector subtraction: $$\Delta \vec{r} = \vec{r}_{	ext{fin}} - \vec{r}_{	ext{ini}}$$

Question 15

A ball is thrown from $$\vec{r}_{	ext{ini}} = (0,0) m to$$ $$\vec{r}_{	ext{fin}} = (10,0) m in 5 $$seconds. What is its average velocity?

Accepted Answer

$$(2, 0) m/s$$

Question 16

Which of the following is true about vector subtraction?

Accepted Answer

It gives a vector pointing from the tip of the subtracted vector to the tip of the first vector.

Question 17

A student walks from $$\vec{r}_1 = (2, 1) m to$$ $$\vec{r}_2 = (5, 5) m in 2 $$seconds. What is the average velocity vector?

Accepted Answer

$$(1.5, 2) m/s$$

Question 18

If $$\vec{A} = (4, 3)$$ and you multiply it by the scalar $$0.5$$, what is the resulting vector?

Accepted Answer

$$(2, 1.5)$$

Question 19

Which formula would you use to calculate the average velocity of a moving object?

Accepted Answer

$$\vec{v}_{	ext{avg}} = \frac{\Delta \vec{r}}{\Delta t}$$

Vectors, Displacement, and Velocity in Physics

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