AP Physics C: Mechanics Practice Quiz: Scalars and Vectors

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 11 questions to check your progress.

Question 1 of 11

Which of the following best describes a scalar quantity?

A)A quantity described by magnitude only.B)A quantity described by direction only.C)A quantity described by both magnitude and direction.D)A quantity that is the sum of other quantities.

All Questions (11)

Which of the following best describes a scalar quantity?

A) A quantity described by magnitude only.

B) A quantity described by direction only.

C) A quantity described by both magnitude and direction.

D) A quantity that is the sum of other quantities.

Correct Answer: A

Based on the provided content, 'Scalars are quantities described by magnitude only.' Option C describes a vector.

A physical quantity is classified as a vector if it is described by which of the following?

A) Magnitude only.

B) Direction only.

C) Both magnitude and direction.

D) Its components in unit vector notation.

Correct Answer: C

The provided content states that 'vectors are quantities described by both magnitude and direction.' While unit vector notation is a way to express a vector, the fundamental definition involves magnitude and direction.

A measurement is recorded as '25 meters, downward.' How should this quantity be classified?

A) As a scalar, because it has a magnitude.

B) As a vector, because it has both a magnitude and a direction.

C) As a scalar, because it does not use unit vector notation.

D) As a resultant vector, because it is a single measurement.

Correct Answer: B

The measurement includes a magnitude ('25 meters') and a direction ('downward'). According to the definition, quantities with both magnitude and direction are vectors.

When a vector is visually modeled as an arrow, what property of the arrow is proportional to the vector's magnitude?

A) The thickness of the arrow's line.

B) The angle the arrow makes with an axis.

C) The length of the arrow.

D) The color of the arrow.

Correct Answer: C

The provided content states that vectors can be modeled as arrows with 'lengths proportional to their magnitude.' The angle of the arrow represents the vector's direction.

A vector is expressed in unit vector notation as $\vec{r}=(7\hat{i} - 3\hat{j})$. What does the term '-3$\hat{j}$' represent?

A) The total magnitude of the vector.

B) The direction of the vector.

C) The component of the vector in the x-direction.

D) The component of the vector in the y-direction.

Correct Answer: D

In the standard unit vector notation $\vec{r}=(A\hat{i}+B\hat{j}+C\hat{k})$, the term with the unit vector $\hat{j}$ represents the component along the y-axis. Therefore, -3$\hat{j}$ is the y-component of the vector.

Given two vectors, $\vec{A} = (2\hat{i} + 5\hat{j})$ and $\vec{B} = (4\hat{i} - 2\hat{j})$, what is the resultant vector $\vec{C} = \vec{A} + \vec{B}$?

A) $\vec{C} = (2\hat{i} + 7\hat{j})$

B) $\vec{C} = (6\hat{i} - 3\hat{j})$

C) $\vec{C} = (8\hat{i} - 10\hat{j})$

D) $\vec{C} = (6\hat{i} + 3\hat{j})$

Correct Answer: D

To find the resultant vector, we sum the corresponding components of the addend vectors. Using the equation $\vec{C}=(A_{x}+B_{x})\hat{i}+(A_{y}+B_{y})\hat{j}$, we get $C_x = 2 + 4 = 6$ and $C_y = 5 + (-2) = 3$. Therefore, $\vec{C} = (6\hat{i} + 3\hat{j})$.

According to the provided content, what is a resultant vector?

A) A vector that has a magnitude of one.

B) The vector sum of the addend vectors' components.

C) A vector that has been broken down into its components.

D) A visual model of a vector using an arrow.

Correct Answer: B

The content explicitly defines a resultant vector as 'the vector sum of the addend vectors' components.' This means it is the single vector that results from adding two or more vectors together.

Two vectors, $\vec{P}$ and $\vec{Q}$, are represented by arrows. The arrow for $\vec{P}$ is half as long as the arrow for $\vec{Q}$, and they point in opposite directions. Which statement correctly describes the relationship between the two vectors?

A) The magnitude of $\vec{P}$ is twice the magnitude of $\vec{Q}$, and their directions are the same.

B) The magnitude of $\vec{P}$ is half the magnitude of $\vec{Q}$, and their directions are opposite.

C) The magnitude of $\vec{P}$ is half the magnitude of $\vec{Q}$, and their directions are the same.

D) The magnitudes of $\vec{P}$ and $\vec{Q}$ are equal, but their directions are opposite.

Correct Answer: B

The content states that the length of the arrow is proportional to the magnitude, and the arrow shows the direction. Since the arrow for $\vec{P}$ is half as long, its magnitude is half that of $\vec{Q}$. Since they point in opposite directions, their directions are opposite.

Consider two vectors in three-dimensional space: $\vec{A} = (5\hat{i} - 1\hat{j} + 2\hat{k})$ and $\vec{B} = (-2\hat{i} + 3\hat{j} - 4\hat{k})$. What is their resultant vector sum, $\vec{C}$?

A) $\vec{C} = (7\hat{i} - 4\hat{j} + 6\hat{k})$

B) $\vec{C} = (3\hat{i} + 2\hat{j} - 2\hat{k})$

C) $\vec{C} = (3\hat{i} + 2\hat{j} + 2\hat{k})$

D) $\vec{C} = (-10\hat{i} - 3\hat{j} - 8\hat{k})$

Correct Answer: B

The principle of adding components applies to three dimensions. We sum the $\hat{i}$, $\hat{j}$, and $\hat{k}$ components separately. $C_x = 5 + (-2) = 3$. $C_y = -1 + 3 = 2$. $C_z = 2 + (-4) = -2$. The resultant vector is $\vec{C} = (3\hat{i} + 2\hat{j} - 2\hat{k})$.

A weather report states the temperature is 22 degrees Celsius. Which of the following correctly identifies this measurement?

A) It is a vector, because it describes an environmental condition.

B) It is a scalar, because it only provides a magnitude without a direction.

C) It is a vector, because temperature can be negative.

D) It is a resultant vector, because it is an average.

Correct Answer: B

The reading '22 degrees Celsius' is a magnitude. It does not have an associated direction (e.g., north, up, down). Since it is described by magnitude only, it is a scalar quantity.

A resultant vector is given by the equation $\vec{C}=(A_{x}+B_{x})\hat{i}+(A_{y}+B_{y})\hat{j}$. What does the term $(A_{x}+B_{x})$ represent?

A) The total magnitude of the resultant vector $\vec{C}$.

B) The magnitude of the x-component of the resultant vector $\vec{C}$.

C) The magnitude of the x-component of the addend vector $\vec{A}$.

D) The direction of the resultant vector $\vec{C}$.

Correct Answer: B

The equation shows that the resultant vector $\vec{C}$ is formed by summing the components of the addend vectors $\vec{A}$ and $\vec{B}$. The term multiplying the $\hat{i}$ unit vector is the x-component of the resultant vector. Therefore, $(A_{x}+B_{x})$ is the magnitude of the x-component of $\vec{C}$.