AP Physics C: Mechanics Practice Test (2027)

A linear-air-track apparatus in Dr. Okafor's lab automatically fits a polynomial curve to the position-versus-time data of a glider. For one trial, the software's best-fit position function is reported as: x(t) = 5t³ − 2t² + 7 where x is in meters and t is in seconds. The lab instructions ask each group to report the instantaneous-velocity function that corresponds to this fitted position expression, then use it on a later page to evaluate v(t) at specific times of interest.

Based on the fitted position function, what is the instantaneous-velocity function v(t) of the glider?

A position-time graph for an object moving along a straight line is shown. The graph starts at x=0, increases quadratically to a maximum positive position, and then decreases quadratically back towards x=0, forming an inverted parabola.

Which of the following statements best describes the object's motion?

A ball is launched from the ground with an initial speed of 25 m/s at an angle of 37° above the horizontal (sin 37° ≈ 0.60, cos 37° ≈ 0.80). Taking g = 10 m/s² and neglecting air resistance, how long is the ball in the air before it returns to the ground?

The velocity of a particle moving along the x-axis is given by v(t) = 3t² + 4t, where v is in m/s and t is in seconds. If the particle starts at x(0) = 0 m, what is its position function x(t)?

A motorcycle traveling at 30 m/s applies its brakes and decelerates uniformly at 5 m/s² until it stops. What distance does the motorcycle travel during braking?

A velocity-time graph for an object moving along a straight line is shown. From t=0s to t=2s, the velocity is a constant +10 m/s. From t=2s to t=4s, the velocity decreases linearly from +10 m/s to 0 m/s.

What is the total displacement of the object from t = 0 s to t = 4 s?

A car's position is recorded at various times: Time (s) | Position (m) ---|--- 0 | 0 1 | 5 2 | 20 3 | 45

What is the average acceleration of the car between t = 1 s and t = 3 s?

In projectile motion, assuming no air resistance, which of the following statements about the horizontal and vertical components of velocity is true?

During a motion-tracking lab, student Priya walks in a straight line 6.0 m due East across the classroom floor, pauses to reset her stopwatch, and then walks 8.0 m due North along a perpendicular chalk line. Her lab partner records the ending point relative to the origin marked at her starting position. The total path length on the data sheet reads 14.0 m, and the lab rubric asks for 'the straight-line distance from start to finish' (the magnitude of the position-vector change).

What is the magnitude of Priya's total displacement from her starting point?

A boat can travel at 4.0 m/s relative to the water. It attempts to cross a river 100 m wide. The river current flows downstream (perpendicular to the boat's intended path) at a speed of 3.0 m/s relative to the riverbank. The boat points its bow directly across the river.

What is the magnitude of the boat's velocity relative to the riverbank?

On a position-time graph, what does the slope of the line at any given point represent?

A projectile is launched from the ground and follows a parabolic path, neglecting air resistance. At the highest point of its trajectory, what are the magnitudes of its velocity and acceleration?

A cannonball is fired horizontally from the top of a cliff 125 m high with an initial speed of 25 m/s. Assume the acceleration due to gravity is 10 m/s² downwards and neglect air resistance.

What is the horizontal range of the cannonball from the base of the cliff?

An airplane needs to fly due North at a speed of 200 km/h relative to the ground. There is a wind blowing from the West at 50 km/h. What should be the airplane's airspeed (speed relative to the air) and its heading (direction relative to the air)?

A car accelerates uniformly from rest at 3.0 m/s² for a distance of 50 m. Which kinematic equation is most appropriate to find the car's final speed?

Which of the following statements correctly differentiates between average velocity and instantaneous velocity?

Which of the following statements correctly distinguishes between speed and velocity?

On a velocity-time graph, what does the slope of the line at any given point represent?

A particle moves along the x-axis with acceleration a(t) = (12t − 6) m/s². At t = 0 its velocity is −2 m/s and its position is 5 m. What is the particle's position at t = 2 s?

If the position of an object is described by a function x(t), which mathematical operation must be performed to determine its instantaneous acceleration?