AP Physics 1 FRQ practice

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🎡AP Physics 1

Practice FRQ 1 of 111/11

2. A student rolls a small cart across a large, level gym floor while another student observes from a moving walkway, as shown in Figure 1.

Figure 1. Cart motion on the gym floor in inertial frame S at three times (t = 0 s, 2.0 s, 4.0 s), with constant velocity components v_x = 2.0 m/s east and v_y = 1.5 m/s north.

Figure 2. Graph axes for v_x versus time t in frame S (0 to 4.0 s).

Figure 3. Graph axes for v_y versus time t in frame S (0 to 4.0 s).

Draw the cart's velocity components as functions of time in frame $S$ . In frame $S$ , the cart moves with constant velocity components $v_x=2.0\ \text{m/s}$ and $v_y=1.5\ \text{m/s}$ for the time interval from $t=0$ to $t=4.0\ \text{s}$ .

• On Figure 2, draw a graph of $v_x(t)$ from $t=0$ to $t=4.0\ \text{s}$ .
• On Figure 3, draw a graph of $v_y(t)$ from $t=0$ to $t=4.0\ \text{s}$ .
Be sure to label any nonzero constant values on each graph.

Figure 4. Velocity vector decomposition in frames S and S′ for relative motion (S′ moving east at v_{S′/S} = 1.0 m/s).

Starting with the definition of relative velocity in one dimension and vector addition, derive expressions for the cart's velocity components $v'_x$ and $v'_y$ as measured in $S'$ . Then derive an expression for the magnitude $v'$ of the cart's velocity in $S'$ . The moving walkway frame $S'$ moves east at $v_{S'/S}=1.0\ \text{m/s}$ relative to frame $S$ . At $t=0$ , the origins of $S$ and $S'$ coincide.

Express your final answers in terms of $v_x$ , $v_y$ , and $v_{S'/S}$ . Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Using Figure 4, draw and label the velocity vector components.

Figure 5. Graph axes for x′ versus time t in frame S′ (0 to 4.0 s).

Figure 6. Graph axes for y′ versus time t in frame S′ (0 to 4.0 s).

Assume the cart continues moving with the same constant velocity components in frame $S$ for $0≤ t≤ 4.0\ \text{s}$ and that $S'$ continues moving at constant speed relative to $S$ . The position of the cart at $t=0$ is the origin in both frames.

Sketch and label a graph of $x'(t)$ on Figure 5 for the cart from $t=0$ to $t=4.0\ \text{s}$ .

ii.

Sketch and label a graph of $y'(t)$ on Figure 6 for the cart from $t=0$ to $t=4.0\ \text{s}$ .

Indicate whether the magnitude of the cart's average velocity from $t=1.0\ \text{s}$ to $t=4.0\ \text{s}$ as measured in frame $S'$ is greater than, less than, or equal to the magnitude of the cart's average velocity over the same interval as measured in frame $S$ . Consider the cart's motion over the interval from $t=1.0\ \text{s}$ to $t=4.0\ \text{s}$ .
Given values: $v_x=2.0\ \text{m/s}$ , $v_y=1.5\ \text{m/s}$ , $v_{S'/S}=1.0\ \text{m/s}$ .

$\left|\vec{v}_{\text{avg}}\right|' > \left|\vec{v}_{\text{avg}}\right|$
$\left|\vec{v}_{\text{avg}}\right|' < \left|\vec{v}_{\text{avg}}\right|$
$\left|\vec{v}_{\text{avg}}\right|' = \left|\vec{v}_{\text{avg}}\right|$
Justify how your response is consistent with the position-versus-time graphs you sketched in part C.

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