AP Physics 1 FRQ Practice

🎡AP Physics 1

Practice FRQ 1 of 171/17

1. A student rolls a small puck across a smooth horizontal air table. At the instant shown in Figure 1, the puck is at point P. An observer in the lab frame measures the puck’s velocity to have magnitude 2.0 m/s directed 30° north of east. A second observer is in a cart that moves with constant velocity 1.2 m/s due east relative to the lab.

Figure 1. Puck velocity in the lab frame and cart velocity relative to the lab (top view).

Top-down (plan) view of a rectangular horizontal air table occupying most of the figure.

Air table and background:
- Draw a clean, light-gray rectangle representing the air table, centered on the page, with a thin black outline.
- No texture; the surface is smooth.

Point P (puck position):
- Mark a single point labeled "P".
- Place P slightly left of the table’s center and slightly below the table’s horizontal midline (so it is clearly not on an edge and leaves room to draw vectors to the right and upward).
- Depict P as a small solid black dot.

Coordinate axes (lab frame):
- Draw x–y axes with the origin located exactly at point P (the axes cross at P).
- +x axis: a straight horizontal arrow extending to the right from P, labeled "+x (east)" near the arrowhead.
- +y axis: a straight vertical arrow extending upward from P, labeled "+y (north)" near the arrowhead.
- The axes are perpendicular and visually prominent (slightly thicker than the table outline).

Puck velocity vector in the lab frame:
- From point P, draw a single solid arrow representing the puck’s velocity in the lab frame.
- The arrow must make an angle of exactly 30° measured counterclockwise from the +x axis (i.e., 30° above the horizontal +x direction, pointing into the first quadrant).
- Place a small angle marker at P between the +x axis and the velocity vector, and label the angle marker with the visible text "30°".
- Label the velocity vector with the visible text "2.0 m/s" placed just above the arrow’s midpoint, aligned with the arrow direction.

Cart velocity arrow (cart relative to lab):
- Draw a second arrow that is purely horizontal, pointing due east (exactly parallel to +x).
- Place this cart-velocity arrow in the upper-right region of the table area so it does not overlap point P, the coordinate axes, or the puck velocity vector.
- Label this arrow with visible text "v_cart = 1.2 m/s" positioned just above the arrow’s midpoint.

Vector scaling constraint (to enforce numerical accuracy):
- The two velocity arrows must be drawn to a common scale so their lengths reflect their magnitudes.
- Specifically: the length of the cart-velocity arrow must be exactly 0.60 times the length of the puck’s 2.0 m/s velocity arrow (since 1.2/2.0 = 0.60).

Clarity constraints:
- Only the items listed above appear: the table rectangle, point P, the x–y axes through P, the 30° puck velocity arrow labeled "2.0 m/s", and the separate eastward cart arrow labeled "v_cart = 1.2 m/s".
- No extra points, no additional velocities, and no title text other than the labels specified.

Figure 2. Axes for graphing the lab-frame y-component of velocity, v_y, from t = 0 to 4.0 s.

A blank set of graph axes with gridlines, prepared for a v_y versus t sketch.

Overall layout:
- The graph occupies most of the figure, with the axes centered and a light square grid covering the plotting area.

Axes (all required features included):
- Horizontal axis label: "t (s)" centered below the axis.
- Horizontal axis range: from 0 to 4.0.
- Horizontal tick marks and labels: ticks at every 1.0 s, with numeric labels shown at 0, 1.0, 2.0, 3.0, and 4.0.
- Vertical axis label: "v_y (m/s)" centered along the vertical axis.
- Vertical axis range: from −2.0 to +2.0.
- Vertical tick marks and labels: ticks at every 0.5 m/s, with numeric labels shown at −2.0, −1.5, −1.0, −0.5, 0, +0.5, +1.0, +1.5, and +2.0.
- Origin labeling: the intersection of the axes is explicitly labeled with the visible text "0" (at the v_y = 0 line and t = 0).
- Arrows: place arrowheads on the positive ends of both axes (right end of the t-axis, top end of the v_y-axis).

Gridlines:
- Light gray vertical gridlines aligned with each 0.5 s subdivision (minor grid) and darker gray gridlines aligned with each 1.0 s tick (major grid).
- Light gray horizontal gridlines aligned with each 0.5 m/s tick.

Curve/plot content:
- No curve is drawn in this figure (axes-only template). No points, no line segments, and no annotations other than axis labels, tick labels, and the origin label.

Numerical accuracy constraint (implicit from axes choice):
- The y-axis scale is chosen to cleanly include the expected constant lab-frame value v_y = 2.0·sin(30°) = 1.0 m/s without crowding, so +1.0 m/s is a labeled tick mark on the axis.

On the axes shown in Figure 2, sketch a graph of the y-component of the puck’s velocity $v_y$ as a function of time $t$ from $t = 0$ to $t = 4.0\ \text{s}$ , as measured in the lab frame.

ii.

Derive an expression for the x- and y-components of the puck’s displacement $\Delta \vec{r}$ during the interval from $t = 0$ to $t = 4.0\ \text{s}$ as measured in the lab frame. Express your answers in terms of the given speed 2.0 m/s, the angle $30^\circ$ , and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

iii.

Derive an expression for the magnitude of the puck’s average velocity $\left|\vec{v}_{\text{avg}}\right|$ over the interval from $t = 0$ to $t = 4.0\ \text{s}$ as measured in the lab frame. Express your answer in terms of the given speed 2.0 m/s and the angle $30^\circ$ . Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Indicate whether the magnitude of the puck’s velocity as measured by the cart observer is greater than, less than, or equal to 2.0 m/s. The cart observer measures positions using axes that remain parallel to the lab axes. The cart moves with constant velocity 1.2 m/s due east relative to the lab for the entire 4.0 s interval.

Greater than 2.0 m/s
Less than 2.0 m/s
Equal to 2.0 m/s
Justify your response by using one-dimensional vector addition for the x-components and by referencing the puck’s y-component of velocity.