AP Physics C: Mechanics Practice Quiz: Displacement, Velocity, and Acceleration
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
All Questions (16)
A) The total distance an object has traveled.
B) The change in an object's position from a starting point to an ending point.
C) How fast an object is moving.
D) The rate at which an object's velocity changes.
Correct Answer: B
The provided content defines displacement as 'the change in an object's position.' This corresponds directly to option B.
A) Δx = x + x₀
B) Δx = x₀ - x
C) Δx = x * x₀
D) Δx = x - x₀
Correct Answer: D
The content provides the relevant equation for displacement as Δx = x - x₀, which is the final position minus the initial position.
A) The rate of change of an object's acceleration.
B) The object's final velocity minus its initial velocity.
C) The displacement of an object divided by the time interval in which the displacement occurs.
D) The derivative of the object's position with respect to time.
Correct Answer: C
The content explicitly states, 'Average velocity is the displacement of an object divided by the interval of time in which that displacement occurs.' Option D describes instantaneous velocity.
A) v_avg = Δx * Δt
B) v_avg = Δt / Δx
C) v_avg = Δx / Δt
D) v_avg = d(x)/dt
Correct Answer: C
The provided content gives the equation for average velocity as v_avg = Δx / Δt. Note that the vector notation is omitted in the options for simplicity, but the relationship is the same.
A) The total displacement over the total time.
B) The velocity of an object over a long period of time.
C) The rate of change of an object's position at a specific moment in time.
D) The change in velocity divided by the change in time.
Correct Answer: C
The content defines instantaneous velocity as 'the rate of change of the object's position,' which implies a specific moment. It is also mathematically defined as the derivative of position with respect to time, which represents an instantaneous rate of change.
A) Integration
B) Division
C) Multiplication
D) Differentiation
Correct Answer: D
The content states that instantaneous velocity 'is equal to the derivative of position with respect to time.' The process of taking a derivative is called differentiation.
A) The rate of change of an object's position.
B) The rate of change of an object's velocity.
C) The total change in an object's position.
D) The average speed over a time interval.
Correct Answer: B
The definition provided is 'Instantaneous acceleration is the rate of change of the object's velocity.'
A) a = dv/dt
B) a = dr/dt
C) a = Δv/Δt
D) a = v * t
Correct Answer: A
The content provides the relevant equation for instantaneous acceleration as a = dv/dt, which is the derivative of velocity with respect to time.
A) By taking the derivative of r(t) with respect to time once.
B) By dividing the displacement by the total time.
C) By taking the derivative of the velocity function, which is itself the derivative of r(t).
D) By integrating the position function r(t) with respect to time.
Correct Answer: C
To find acceleration, one must first find velocity by taking the derivative of position (v = dr/dt). Then, one finds acceleration by taking the derivative of that velocity function (a = dv/dt). Therefore, acceleration is found by taking the derivative of the velocity function.
A) 15 meters
B) -15 meters
C) 5 meters
D) -5 meters
Correct Answer: B
Using the displacement equation Δx = x - x₀, where x = -5 m and x₀ = 10 m. The calculation is Δx = (-5 m) - (10 m) = -15 m.
A) The acceleration must be constant and non-zero.
B) The acceleration must be zero.
C) The acceleration must be increasing.
D) The acceleration must be equal to the velocity.
Correct Answer: B
Acceleration is the rate of change of velocity (a = dv/dt). If velocity is constant, its rate of change is zero. Therefore, the acceleration must be zero.
A) Velocity
B) Acceleration
C) Displacement
D) Time
Correct Answer: C
The first and fourth points of the provided content explicitly define displacement as the 'change in an object's position.'
A) Average velocity is a scalar, while instantaneous velocity is a vector.
B) Average velocity is calculated over a time interval, while instantaneous velocity is at a specific point in time.
C) Average velocity involves position, while instantaneous velocity involves acceleration.
D) There is no fundamental difference; they are interchangeable.
Correct Answer: B
The definitions provided show that average velocity (v_avg = Δx/Δt) is calculated over an interval of time (Δt), whereas instantaneous velocity (v = dr/dt) is the rate of change at a specific moment, which is the limit as Δt approaches zero.
A) The object's displacement.
B) The object's average velocity.
C) The object's instantaneous acceleration.
D) The object's final position.
Correct Answer: C
The content explicitly states that 'Instantaneous acceleration is the rate of change of the object's velocity, which is equal to the derivative of velocity with respect to time.'
A) The object's velocity must be zero.
B) The object's velocity must be constant.
C) The object's velocity is changing.
D) The object's velocity is equal to its position.
Correct Answer: C
Acceleration is defined as the rate of change of velocity. If acceleration is non-zero, it means that the velocity is changing over time.
A) a is the integral of r with respect to t.
B) a is the first derivative of r with respect to t.
C) a is the second derivative of r with respect to t.
D) a is unrelated to r.
Correct Answer: C
Since acceleration (a) is the derivative of velocity (v), and velocity (v) is the derivative of position (r), acceleration is the derivative of the derivative of position. This is known as the second derivative.