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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