AP Physics 1 FRQ Practice

🎡AP Physics 1

Practice FRQ 1 of 201/20

1. A student tracks a small puck sliding on a smooth, level air table. Two observers analyze the puck’s motion: Observer R is at rest with respect to the table, and Observer T is on a cart that moves at constant velocity relative to the table. The positive x-direction is to the right and the positive y-direction is upward on the page, as shown in Figure 1.

Figure 1. Overhead view of puck motion on an air table with two observers (R at rest with table, T on a cart moving right at 4.0 m/s).

$Overhead (top-down) physics diagram on a plain white background with a single rectangular air table and a clearly drawn coordinate system. Table (air table): - Draw a large horizontal rectangle representing the air table occupying most of the figure width. - The table’s long dimension is left-to-right. - The table boundary is a thin black outline. - Centered near the bottom edge of the table, place the label text: "smooth, level air table". Coordinate axes (fixed to the table; Observer R frame): - Place a standard x–y axis cross on the tabletop, located slightly left of the table’s horizontal midpoint and slightly below the table’s vertical midpoint so there is open space to the right for the cart. - Draw the x-axis as a horizontal line with an arrowhead on its right end only. Label the arrow tip with "+x". - Draw the y-axis as a vertical line with an arrowhead on its top end only. Label the arrow tip with "+y". - At the axis intersection, place a small dot and label it "origin". Puck at t = 0: - Draw a small filled circle (the puck) centered exactly on the origin dot. - Place the text label "puck" next to the circle, with a short leader line pointing to it. - Directly below the puck, write "t = 0". Initial velocity of the puck: - From the puck’s center, draw a single straight velocity vector arrow pointing into the first quadrant (up and to the right). - The arrow must make a 45° angle measured from the +x axis toward the +y axis (equal horizontal and vertical components visually). - Label this arrow "\u2192 v (initial)" with the label placed above the arrow shaft, not at the tip. Observer R (rest frame on the table): - Add a small stick-figure icon or simple label near the left side of the table interior (left third of the tabletop), not on the cart. - Label it clearly: "Observer R (at rest with table)". Cart carrying Observer T: - On the right side of the tabletop, draw a cart as a low rectangle with two visible wheels (two circles) beneath it, positioned fully on the table surface. - The cart must be located in the right third of the table, horizontally aligned with the origin (same vertical level as the origin), so the cart appears to the right of the puck. - Place a label centered on the cart body: "Observer T". Cart motion (given speed 4.0 m/s): - From the cart body (starting at the cart’s center), draw a horizontal velocity arrow pointing directly to the right (parallel to the +x axis). - Place the text "4.0 m/s" directly above the middle of this arrow. - Place the text "constant velocity" directly below the same arrow. Global direction reminder: - Near the top-left of the figure (outside the table rectangle), include a small note: "Positive x to the right; positive y upward". Styling constraints: - All arrows are solid black with single arrowheads. - All text is horizontal and fully readable. - No extra objects, no extra forces, and no trajectory curve are drawn in this figure.$

Figure 2. Blank axes for plotting the x-component of velocity v_x versus time t from 0 to 4.0 s (Observer R).

A blank Cartesian graph template (no plotted data curve) with clearly labeled axes, numeric tick labels, and light grid lines.

Axes:
- Horizontal axis labeled exactly: "t (s)".
- Horizontal axis range: from 0 at the origin to 4.0 at the right boundary.
- Horizontal tick marks: labeled at 0, 1.0, 2.0, 3.0, and 4.0 with equal spacing.
- Vertical axis labeled exactly: "v_x (m/s)".
- Vertical axis range: from −6 at the bottom boundary to +6 at the top boundary.
- Vertical tick marks: labeled every 2 m/s at −6, −4, −2, 0, 2, 4, and 6 with equal spacing.
- The origin is explicitly labeled "0" at the intersection of the axes.
- Arrowheads appear only on the positive end of the t-axis (pointing right) and the positive end of the v_x-axis (pointing up).

Grid:
- Add light, evenly spaced grid lines across the entire plotting region.
- Vertical grid lines align with each 1.0 s tick on the t-axis.
- Horizontal grid lines align with each 2 m/s tick on the v_x-axis.

Highlighted time markers required by the prompt:
- Emphasize the vertical grid lines at t = 0, t = 2.0, and t = 4.0 by making those three vertical lines slightly darker than the other grid lines.
- Ensure the tick labels "0", "2.0", and "4.0" on the time axis are clearly readable and correspond to these emphasized grid lines.

Blank-graph constraint:
- Do not draw any curve, line, points, or annotations besides the axes, tick marks, tick labels, axis labels, grid lines, and arrowheads.
- No title is shown inside the graph area.

i. On the axes shown in Figure 2, sketch a graph of the x-component of the puck’s velocity

v_x

as a function of time

t

from

t = 0

t = 4.0\ \text{s}

as measured by Observer R.

ii. Derive an expression for the magnitude of the puck’s average acceleration

a_{\text{avg}}

from

t = 0

t = 2.0\ \text{s}

as measured by Observer R. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

iii. Derive an expression for the puck’s displacement vector

\Delta \vec{r}

from

t = 0

t = 4.0\ \text{s}

as measured by Observer R. Express your final answer in unit-vector form

\Delta \vec{r} = (\Delta x)\hat{i} + (\Delta y)\hat{j}

. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

B. Indicate whether the magnitude of the puck’s velocity as measured by Observer T at

t = 2.0\ \text{s}

is greater than, less than, or equal to the magnitude of the puck’s velocity as measured by Observer R at

t = 2.0\ \text{s}

.
______ Greater than
______ Less than
______ Equal to
Justify your response.

🎡AP Physics 1

Practice FRQ 1 of 201/20

Figure 1. Overhead view of puck motion on an air table with two observers (R at rest with table, T on a cart moving right at 4.0 m/s).

Figure 2. Blank axes for plotting the x-component of velocity v_x versus time t from 0 to 4.0 s (Observer R).

i. On the axes shown in Figure 2, sketch a graph of the x-component of the puck’s velocity

v_x

as a function of time

t

from

t = 0

t = 4.0\ \text{s}

as measured by Observer R.

ii. Derive an expression for the magnitude of the puck’s average acceleration

a_{\text{avg}}

from

t = 0

t = 2.0\ \text{s}

as measured by Observer R. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

iii. Derive an expression for the puck’s displacement vector

\Delta \vec{r}

from

t = 0

t = 4.0\ \text{s}

as measured by Observer R. Express your final answer in unit-vector form

\Delta \vec{r} = (\Delta x)\hat{i} + (\Delta y)\hat{j}

. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

B. Indicate whether the magnitude of the puck’s velocity as measured by Observer T at

t = 2.0\ \text{s}

is greater than, less than, or equal to the magnitude of the puck’s velocity as measured by Observer R at

t = 2.0\ \text{s}

.
______ Greater than
______ Less than
______ Equal to
Justify your response.