AP Physics 1: Algebra-Based Practice Quiz: Scalars and Vectors in One Dimension

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

Test your understanding with short quizzes. This quiz has 16 questions to check your progress.

Question 1 of 16

Which of the following best describes a scalar quantity?

A)A quantity described by both magnitude and direction.B)A quantity described by magnitude only.C)A quantity described by direction only.D)A quantity that can only be positive.

All Questions (16)

Which of the following best describes a scalar quantity?

A) A quantity described by both magnitude and direction.

B) A quantity described by magnitude only.

C) A quantity described by direction only.

D) A quantity that can only be positive.

Correct Answer: B

Based on the provided content, scalars are quantities described by magnitude (a numerical value) only. Vectors require both magnitude and direction.

A student is asked to identify a vector quantity from a list. Which of the following is a vector?

A) The speed of a car, 25 m/s.

B) The distance a person walked, 500 meters.

C) The mass of a block, 10 kg.

D) The acceleration of a falling object, 9.8 m/s² downward.

Correct Answer: D

Acceleration is a vector quantity because it has both magnitude (9.8 m/s²) and direction (downward). Speed and distance are listed as examples of scalar quantities.

In a one-dimensional coordinate system where 'right' is the positive direction, a car moves from a position of +10 m to a position of -5 m. What is the car's displacement?

A) +15 m

B) -15 m

C) +5 m

D) -5 m

Correct Answer: B

Displacement is a vector quantity representing the change in position (final position - initial position). The calculation is a vector sum: (-5 m) - (+10 m) = -15 m. The negative sign indicates the displacement is in the negative direction (left).

How is a vector visually modeled to represent its magnitude and direction?

A) As a point on a graph, where the coordinates give magnitude and direction.

B) As a number with a positive or negative sign.

C) As an arrow with a length proportional to its magnitude and pointing in its direction.

D) As a scalar value multiplied by a unit of time.

Correct Answer: C

The content states that vectors can be visually modeled as arrows. The length of the arrow is proportional to the vector's magnitude, and the way the arrow points indicates the vector's direction.

A person walks 8 meters east and then 5 meters west. If the eastward direction is defined as positive, what is the vector sum of these two displacements?

A) +13 m

B) -13 m

C) +3 m

D) -3 m

Correct Answer: C

In the given one-dimensional coordinate system, the eastward displacement is +8 m. The westward displacement is in the opposite direction, so it is denoted by a negative sign, -5 m. The vector sum is (+8 m) + (-5 m) = +3 m.

In one-dimensional motion, an object's velocity is recorded as -15 m/s. What does the negative sign indicate?

A) The object is slowing down.

B) The magnitude of the velocity is 15 m/s.

C) The direction of the velocity is opposite to the defined positive direction.

D) The object's acceleration is negative.

Correct Answer: C

The content specifies that in one dimension, the sign of a vector component completely describes its direction. A negative sign indicates that the vector points in the direction opposite to the one defined as positive for that coordinate system.

An athlete runs exactly one lap around a 400-meter track, ending at the starting line. Which statement correctly describes the distance traveled and the displacement?

A) The distance is 400 m, and the displacement is 400 m.

B) The distance is 0 m, and the displacement is 400 m.

C) The distance is 400 m, and the displacement is 0 m.

D) The distance is 0 m, and the displacement is 0 m.

Correct Answer: C

Distance is a scalar representing the total path length, which is 400 m. Displacement is a vector representing the change in position from the start point to the end point. Since the athlete finished at the starting point, the net change in position is zero.

Which of the following pairs contains one scalar and one vector quantity?

A) Distance and Speed

B) Position and Displacement

C) Speed and Velocity

D) Velocity and Acceleration

Correct Answer: C

According to the provided content, speed is a scalar quantity (magnitude only), while velocity is a vector quantity (magnitude and direction). The other pairs consist of two scalars (A) or two vectors (B, D).

A ball is thrown upward. At its highest point, its instantaneous velocity is 0 m/s. On its way down, its velocity is -10 m/s. What is the change in velocity from the highest point to this point on the way down?

A) +10 m/s

B) -10 m/s

C) 0 m/s

D) Cannot be determined

Correct Answer: B

The change in velocity is a vector sum: final velocity minus initial velocity. In this one-dimensional case, Change = (-10 m/s) - (0 m/s) = -10 m/s.

A car moving in the positive direction applies its brakes and slows down. What are the signs of the car's velocity and acceleration components?

A) Velocity is positive, acceleration is positive.

B) Velocity is positive, acceleration is negative.

C) Velocity is negative, acceleration is positive.

D) Velocity is negative, acceleration is negative.

Correct Answer: B

The car is moving in the positive direction, so its velocity is positive. Because it is slowing down, its acceleration must be in the opposite direction to its velocity. Therefore, the acceleration is negative.

A vector quantity is defined as a quantity that has...

A) only magnitude.

B) only direction.

C) both magnitude and direction.

D) a standard unit in the SI system.

Correct Answer: C

This is the fundamental definition of a vector provided in the content. Vectors are quantities described by both magnitude and direction.

If a velocity vector is represented by an arrow of length 5 cm pointing to the left, how would you represent a velocity with half the magnitude and in the opposite direction?

A) An arrow of length 2.5 cm pointing to the left.

B) An arrow of length 10 cm pointing to the right.

C) An arrow of length 5 cm pointing to the right.

D) An arrow of length 2.5 cm pointing to the right.

Correct Answer: D

The new vector has half the magnitude, so its arrow should be half the length (2.5 cm). It is in the opposite direction, so if the original pointed left, the new one must point right.

A toy train moves along a straight track. Its initial velocity is +0.5 m/s. It experiences an acceleration of -1.5 m/s². What is the change in velocity after 2 seconds? (Note: change in velocity = acceleration × time)

A) -3.0 m/s

B) -2.5 m/s

C) -1.0 m/s

D) +3.0 m/s

Correct Answer: A

The change in velocity is the product of the acceleration vector and the time scalar. The calculation is a one-dimensional vector operation: (-1.5 m/s²) * (2 s) = -3.0 m/s. The initial velocity is not needed to find the change in velocity.

Which statement is true regarding vector representation in one dimension?

A) Vector notation with arrows is always required.

B) The sign of the component (+ or -) is sufficient to describe the direction.

C) Only positive numbers can be used for vector components.

D) The magnitude of a vector is always larger than its component.

Correct Answer: B

The provided content explicitly states that in one dimension, the sign of the component completely describes the direction of that component, and formal vector notation is not required.

An elevator moves from the 1st floor to the 10th floor, and then back down to the 3rd floor. Let the upward direction be positive. Which of the following represents the total displacement?

A) A vector sum resulting in a final position on the 2nd floor.

B) A vector sum resulting in a final position on the 3rd floor.

C) A scalar sum of 16 floors.

D) A vector sum of (+9 floors) + (-7 floors).

Correct Answer: D

Displacement is a vector. The first movement is from 1 to 10, which is a displacement of +9 floors. The second movement is from 10 to 3, which is a displacement of -7 floors. The total displacement is the vector sum of these two individual displacements.

A car's velocity changes from +20 m/s to +10 m/s. What is the change in velocity?

A) +30 m/s

B) +10 m/s

C) -10 m/s

D) -30 m/s

Correct Answer: C

The change in velocity is a vector sum defined as final velocity minus initial velocity. Δv = v_final - v_initial = (+10 m/s) - (+20 m/s) = -10 m/s. The negative sign indicates the change was in the negative direction, causing the car to slow down.