AP Physics 1: Algebra-Based Practice Quiz: Reference Frames and Relative Motion

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

A passenger is sitting still on a bus that is traveling down a straight highway at a constant speed. Which of the following best describes the passenger's reference frame?

A)The highway itself.B)The bus on which the passenger is sitting.C)The final destination of the bus.D)The center of the Earth.

All Questions (16)

A passenger is sitting still on a bus that is traveling down a straight highway at a constant speed. Which of the following best describes the passenger's reference frame?

A) The highway itself.

B) The bus on which the passenger is sitting.

C) The final destination of the bus.

D) The center of the Earth.

Correct Answer: B

An observer's reference frame is the coordinate system or set of axes within which they are stationary. For the passenger, their immediate, non-moving surroundings are the interior of the bus.

A person walks forward at 1 m/s on a train moving forward at 15 m/s relative to the ground. How would an observer standing stationary on the ground describe the motion of the person on the train?

A) The person is moving forward at 1 m/s.

B) The person is moving forward at 14 m/s.

C) The person is moving forward at 15 m/s.

D) The person is moving forward at 16 m/s.

Correct Answer: D

The observed velocity of an object is the vector sum of the object's velocity and the velocity of the observer's reference frame. Since the person and the train are moving in the same direction, their velocities add up: 1 m/s + 15 m/s = 16 m/s.

Two observers are in different inertial reference frames. Observer A is stationary on the ground, and Observer B is in a car moving at a constant velocity of 25 m/s. Both observers watch a ball being dropped from rest. Which physical quantity will both observers measure to be the same for the ball?

A) The initial velocity of the ball.

B) The path taken by the ball.

C) The displacement of the ball.

D) The acceleration of the ball.

Correct Answer: D

The acceleration of any object is the same as measured from all inertial (non-accelerating) reference frames. The initial velocity, path, and displacement will appear different to the two observers because their reference frames are in relative motion.

Car A is traveling east at 20 m/s. Car B is traveling west on the same road at 30 m/s. From the reference frame of the driver in Car A, what is the velocity of Car B?

A) 10 m/s, west

B) 50 m/s, west

C) 10 m/s, east

D) 50 m/s, east

Correct Answer: B

Let east be the positive direction. The velocity of Car A is +20 m/s and Car B is -30 m/s. The velocity of B relative to A is V_B - V_A = (-30 m/s) - (+20 m/s) = -50 m/s. The negative sign indicates the direction is west.

An observer's choice of reference frame will determine the measured value of which of the following pairs of quantities?

A) Mass and acceleration

B) Velocity and mass

C) Velocity and position

D) Acceleration and time

Correct Answer: C

The choice of reference frame defines the origin (affecting position) and the state of motion of the observer (affecting velocity). In AP Physics 1, mass and time are considered absolute, and acceleration is the same in all inertial reference frames.

A boat travels upstream at a speed of 4 m/s relative to the water. The river's current flows downstream at 3 m/s relative to the bank. What is the velocity of the boat as measured by an observer standing on the riverbank?

A) 1 m/s, upstream

B) 1 m/s, downstream

C) 7 m/s, upstream

D) 7 m/s, downstream

Correct Answer: A

Let the upstream direction be positive. The boat's velocity relative to the water is +4 m/s. The water's velocity relative to the bank is -3 m/s (downstream). The boat's velocity relative to the bank is the vector sum: (+4 m/s) + (-3 m/s) = +1 m/s, which is 1 m/s upstream.

A student is in an elevator moving upward at a constant velocity. She drops a coin. A second student is standing stationary on the ground floor and observes the same coin being dropped. How do their measured values of the coin's acceleration compare?

A) The student in the elevator measures a larger acceleration.

B) The student on the ground floor measures a larger acceleration.

C) Both students measure the same non-zero acceleration.

D) The student in the elevator measures zero acceleration.

Correct Answer: C

An elevator moving at a constant velocity is an inertial reference frame, just like the stationary ground floor. The acceleration of an object due to gravity is the same as measured from all inertial reference frames.

A person on a moving walkway walks in the opposite direction of the walkway's motion. The person's speed relative to the walkway is 1.5 m/s. An observer standing still on the ground measures the person's speed to be 1.0 m/s. What is the speed of the moving walkway relative to the ground?

A) 0.5 m/s

B) 1.5 m/s

C) 2.5 m/s

D) 4.0 m/s

Correct Answer: C

Let the direction of the walkway be positive. V_pg = +1.0 m/s. The person walks opposite, so V_pw = -1.5 m/s. The formula is V_pg = V_pw + V_wg. So, +1.0 m/s = -1.5 m/s + V_wg. Solving for V_wg gives V_wg = 2.5 m/s.

A ball is thrown straight up inside a train car that is moving at a constant velocity to the right. From the perspective of an observer standing on the ground outside the train, what is the path of the ball after it leaves the thrower's hand?

A) A straight line up and then straight down.

B) A parabolic arc.

C) A straight line angled upwards and to the right.

D) A circle.

Correct Answer: B

To the observer on the ground, the ball has an initial upward velocity from the throw and a constant horizontal velocity equal to that of the train. The combination of motion with constant horizontal velocity and constant downward vertical acceleration results in a parabolic trajectory.

Which of the following observers is in a non-inertial reference frame?

A) A passenger on a train moving at a constant 80 km/h on a straight track.

B) A pilot in a plane flying at a constant velocity and constant altitude.

C) A driver in a car that is rounding a curve at a constant speed.

D) A person standing still on the ground (approximating the Earth as inertial).

Correct Answer: C

An inertial reference frame is one that is not accelerating. A car rounding a curve is accelerating (centripetal acceleration) because its direction of velocity is changing, even if its speed is constant. Therefore, it is a non-inertial reference frame.

A child on a skateboard is rolling east at 2 m/s. The child throws a ball backward (west) with a speed of 5 m/s relative to the skateboard. What is the velocity of the ball as measured by a stationary observer on the sidewalk?

A) 3 m/s, west

B) 3 m/s, east

C) 7 m/s, west

D) 7 m/s, east

Correct Answer: A

Let east be the positive direction. The skateboard's velocity is +2 m/s. The ball's velocity relative to the skateboard is -5 m/s. The ball's velocity relative to the ground is the vector sum: (+2 m/s) + (-5 m/s) = -3 m/s. The negative sign indicates the direction is west.

Two spaceships, A and B, are moving in the same direction. From the reference frame of a stationary space station, Ship A has a velocity of +v and Ship B has a velocity of +3v. What is the velocity of Ship B as measured by an observer in Ship A?

A) +v

B) +2v

C) +3v

D) +4v

Correct Answer: B

The velocity of B relative to A (V_BA) is given by the formula V_BA = V_B - V_A. Given the velocities relative to the station, V_BA = (+3v) - (+v) = +2v. The observer in Ship A sees Ship B moving away from them in the positive direction at a speed of 2v.

Observer 1 is in a car moving east at a constant 20 m/s. Observer 2 is in a truck moving west at a constant 10 m/s. Both observe a bird flying. Which of the following statements is true regarding the measurements made by the two observers?

A) They must measure the same velocity for the bird but a different acceleration.

B) They must measure the same acceleration for the bird but a different velocity.

C) They must measure the same velocity and the same acceleration for the bird.

D) They must measure a different velocity and a different acceleration for the bird.

Correct Answer: B

Both the car and the truck are moving at constant velocities, so they are inertial reference frames. In inertial reference frames, the measured acceleration of an object is the same for all observers. However, because the observers are moving relative to each other, they will measure different velocities for the bird.

A train is moving east at 25 m/s. A passenger walks from the back of a train car to the front (east) at a speed of 1 m/s relative to the train. The passenger then turns around and walks to the back of the car at the same speed. What is the difference in the magnitude of the passenger's velocity relative to the ground between the two cases?

A) 0 m/s

B) 1 m/s

C) 2 m/s

D) 26 m/s

Correct Answer: C

Let east be positive. Case 1 (walking east): V_ground = 25 m/s + 1 m/s = 26 m/s. Case 2 (walking west): V_ground = 25 m/s - 1 m/s = 24 m/s. The difference in the magnitudes is 26 m/s - 24 m/s = 2 m/s.

A person is juggling balls inside a windowless room. They observe the balls following perfect vertical paths. Based solely on this observation, which of the following can the person conclude about the motion of the room?

A) The room must be stationary.

B) The room must be moving at a constant velocity.

C) The room must be accelerating.

D) The room is an inertial reference frame.

Correct Answer: D

The laws of physics are the same in all inertial reference frames. The observation is consistent with any inertial frame, which includes being stationary or moving at any constant velocity. The person cannot distinguish between these states, but they can conclude they are in a non-accelerating, or inertial, frame.

A car accelerates from rest at a constant rate of 3 m/s². A truck passes the car, moving at a constant velocity of 20 m/s in the same direction. What is the acceleration of the car as measured from the reference frame of the truck driver?

A) 0 m/s²

B) 3 m/s²

C) -17 m/s²

D) 23 m/s²

Correct Answer: B

The truck is moving at a constant velocity, so it is an inertial reference frame. The acceleration of an object is measured to be the same from all inertial reference frames. Since the car's acceleration is 3 m/s² relative to the ground (another inertial frame), the truck driver will also measure its acceleration to be 3 m/s².