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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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FRQ Types & Units

Each FRQ type tests specific skills taught in particular units. Here's why certain units appear for each question type:

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Practice FRQ 1 of 171/17
1. A small drone moves in a horizontal plane at a constant velocity relative to the ground, as shown in Figure 1. The positive x-direction is east and the positive y-direction is north.

Figure 1. Top-down velocity vectors for a drone and a boat in ground (G) and boat (B) reference frames; +x is east and +y is north.

Top-down, clean line diagram on a white background showing a two-dimensional coordinate system and two velocity vectors. Coordinate axes (must be visually dominant): - Draw a horizontal x-axis through the center of the figure with a solid black line. Put a single arrowhead only on the right end to indicate the positive direction. - Draw a vertical y-axis through the same central intersection point (the origin) with a solid black line. Put a single arrowhead only on the top end to indicate the positive direction. - Label the rightward arrow tip of the horizontal axis with the text: "+x (east)" placed just to the right of the arrow tip. - Label the upward arrow tip of the vertical axis with the text: "+y (north)" placed just above the arrow tip. - Mark the axis intersection with a small solid dot (the origin). Do not add any numeric tick marks on these axes. Drone velocity vector (relative to ground): - From the origin dot, draw a solid arrow (medium-thick) pointing into the first quadrant (northeast). - The arrow must make an angle of exactly 30.0° measured counterclockwise from the +x axis to the arrow direction. - Show this angle explicitly using a circular arc centered at the origin, starting along the +x axis and ending on the drone velocity arrow. Place the text "30.0°" adjacent to the arc, inside the first quadrant. - Place the label "12.0 m/s" along the drone arrow, centered on the arrow shaft, with the text parallel to the arrow direction. - Add a small label "Drone" near the arrowhead, offset slightly above the arrow to avoid overlap. Boat velocity vector (relative to ground): - From the same origin dot, draw a second solid arrow (slightly thinner than or equal thickness to the drone arrow) pointing exactly along the +x axis to the right (due east), with no vertical component. - Ensure the boat arrow is shorter than the drone arrow to visually reflect 5.00 m/s compared with 12.0 m/s (the boat arrow length must be 5/12 of the drone arrow length). - Place the label "5.00 m/s" directly above the boat arrow, centered on its length and written horizontally. - Add a small label "Boat" near the boat arrowhead, slightly above and to the right, without touching the axis label. Reference-frame labels: - Place the text "G" (for ground reference frame) in the upper-left region of the diagram (left of the y-axis and above the x-axis), clearly separated from the axes and vectors. - Place the text "B" (for boat reference frame) in the lower-right region of the diagram (right of the y-axis and below the x-axis), clearly separated from the axes and vectors. Styling constraints: - Use black lines and black text only. - No extra objects, no grid, no numerical axis tick marks, and no title beyond the caption. - All text values must match exactly: "12.0 m/s", "5.00 m/s", and "30.0°".

Figure 2. Axes for graphing x-position x (m) versus time t (s) from 0 to 10.0 s.

A blank set of graph axes (no plotted curve) with light grid lines. Axes (REQUIRED exact text and structure): - Horizontal axis: a solid black line along the bottom of the plotting area with an arrowhead only on the right end. Label centered below it: "t (s)". - Horizontal axis numeric range and ticks: start at 0 on the far left and end at 10.0 on the far right. Show exactly three labeled tick marks: "0" at the origin, "4.00" at a point slightly left of the center of the axis, and "10.0" at the far right tick just before the arrowhead. - Vertical axis: a solid black line on the left side of the plotting area with an arrowhead only on the top end. Label rotated vertically (or stacked) beside the axis: "x (m)". - Origin: label the intersection of the two axes with the visible text "0" located at the bottom-left corner where the axes meet. - Vertical axis numeric scale: do not show any numeric tick labels on the vertical axis (leave it unlabeled numerically), but do include evenly spaced tick marks to indicate scale. Grid (REQUIRED): - Add faint, evenly spaced square grid lines across the full plotting rectangle (both vertical and horizontal grid lines). Grid lines must be much lighter than the axis lines. Blank-graph constraints: - Do not draw any curve, points, or markers. - Do not add any additional titles or annotations besides the axis labels and the three x-axis tick labels (0, 4.00, 10.0).
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 in the ground reference frame.
ii. Derive expressions for the x- and y-components of the drone’s velocity in the ground reference frame, vx,Gv_{x,G}vx,G​ and vy,Gv_{y,G}vy,G​, in terms of the given speed 12.0 m/s12.0\ \text{m/s}12.0 m/s and angle 30.0∘30.0^\circ30.0∘. Begin your derivation by writing a fundamental relationship between a vector and its perpendicular components.
iii. Derive an expression for the magnitude of the drone’s displacement Δr⃗\Delta \vec{r}Δr from t=0t = 0t=0 to t=10.0 st = 10.0\ \text{s}t=10.0 s as measured in the ground reference frame. Express your final answer in terms of the given speed 12.0 m/s12.0\ \text{m/s}12.0 m/s, the time interval 10.0 s10.0\ \text{s}10.0 s, and physical constants, as appropriate. Begin your derivation by writing a fundamental kinematics relationship.
B. Indicate whether the magnitude of the drone’s velocity measured in the boat reference frame is less than, greater than, or equal to the magnitude of the drone’s velocity measured in the ground reference frame. An observer on a boat moves due east (positive x-direction) at a constant velocity of 5.00 m/s5.00\ \text{m/s}5.00 m/s relative to the ground. The boat reference frame BBB is inertial. The observer on the boat measures the drone’s velocity relative to the boat as v⃗D/B=v⃗D/G−v⃗B/G\vec{v}_{D/B} = \vec{v}_{D/G} - \vec{v}_{B/G}vD/B​=vD/G​−vB/G​.
______ Less than
______ Greater than
______ Equal to
Justify your response.
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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:

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