⚙️AP Physics C: Mechanics
⚙️AP Physics C: Mechanics
FRQ 1 – Mathematical Routines
Unit 1: Kinematics
FRQ 1 – Mathematical Routines
Unit 1: Kinematics
Practice FRQ 1 of 81/8
1. A small object is launched from ground level at time t = 0 with initial velocity components v_x0 in the horizontal direction and v_y0 in the vertical direction. The object experiences a horizontal acceleration a_x(t) = kt, where k is a positive constant, and a vertical acceleration a_y(t) = -g + bt^2, where b is a positive constant and g is the acceleration due to gravity. The object reaches its maximum height at time t = t_m and returns to ground level at time t = t_e.
Figure 1: Horizontal and vertical velocity components versus time (from launch at t = 0 to landing at t = t_e)
A.
i. On the axes in Figure 1, sketch the horizontal velocity component v_x and the vertical velocity component v_y as functions of time from t = 0 to t = t_e. Clearly indicate the initial values v_x0 and v_y0, and label the time t_m on your graphs where appropriate.
• Your sketches should show the general shape and curvature of each velocity component.
• The relative magnitudes and signs should be consistent with the given accelerations.
ii. Derive an expression for the vertical velocity v_y as a function of time t. Express your answer in terms of v_y0, g, b, t, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.
Figure 2: Ground reference frame (x, y) and observer reference frame (x′, y′) with observer moving at constant speed v_obs in +x
B. Derive an expression for v_x0_prime, the initial horizontal velocity component of the object in the observer's reference frame. Express your answer in terms of v_x0, v_obs, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. An observer moves with constant velocity v_obs = v_x0 in the +x direction relative to the ground frame, as shown in Figure 2. In the observer's reference frame, the object has initial horizontal velocity component v_x0_prime at t = 0.
