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🎡AP Physics 1
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🎡AP Physics 1

FRQ 1 – Mathematical Routines
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Unit 1: Kinematics
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Each FRQ type tests specific skills taught in particular units. Here's why certain units appear for each question type:

This mapping reflects College Board's exam structure - each FRQ type tests specific skills that are taught in particular units.

Practice FRQ 1 of 171/17

1. A drone flies at constant altitude above level ground. The drone's motion is observed by two different inertial observers: Observer G is at rest with respect to the ground, and Observer T is on a truck moving in a straight line along the +x direction. Figure 1 shows the setup.

Figure 1. Top-down reference-frame setup showing ground axes, a truck moving in +x, and the drone velocity relative to the ground.

Figure 1

Figure 2. Axes for sketching x-position versus time for the drone as measured by Observer G.

Figure 2
A.
i.

On the axes shown in Figure 2, sketch a graph of the drone's x-position xxx as a function of time ttt from t=0t = 0t=0 to t=10.0 st = 10.0\ \text{s}t=10.0 s as measured by Observer G. The origin corresponds to the marked point on the ground.

ii.

Derive expressions for the perpendicular components vxv_xvx​ and vyv_yvy​ of the drone's velocity as measured by Observer G in terms of the given speed 12.0 m/s12.0\ \text{m/s}12.0 m/s and angle 30∘30^\circ30∘. Begin your derivation by writing a fundamental relationship between a vector and its components.

iii.

Derive an expression for the drone's displacement magnitude Δr\Delta rΔr from t=0t = 0t=0 to t=10.0 st = 10.0\ \text{s}t=10.0 s as measured by Observer G. Express your answer in terms of the components found in part A.ii and physical constants, as appropriate. Begin your derivation by writing an equation that relates displacement to velocity and time for constant velocity motion.

B.

Indicate whether the x-component of the drone's velocity measured by Observer T, vx, D/Tv_{x,\,D/T}vx,D/T​, is greater than, less than, or equal to the x-component of the drone's velocity measured by Observer G, vx, D/Gv_{x,\,D/G}vx,D/G​. The truck moves with constant velocity v⃗T/G=(8.0 m/s)i^\vec{v}_{T/G} = (8.0\ \text{m/s})\hat{i}vT/G​=(8.0 m/s)i^ relative to the ground. At t=6.0 st = 6.0\ \text{s}t=6.0 s, Observer T measures the drone's velocity relative to the truck.

Greater than
Less than
Equal to
Justify your response using the relationship between velocities measured in different inertial reference frames.

Timed

00:00

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Free Response Question Practice

This practice environment simulates the AP AP Physics 1 Free Response Questions section. Here are some guidelines:

  • Read each question carefullybefore responding. Pay attention to command verbs like "identify," "explain," "analyze," or "evaluate."
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Tip: Answer all parts of each question. Partial credit is often available, so even if you are unsure, provide what you know.