AP Physics 1 FRQ Practice

🎡AP Physics 1

Practice FRQ 1 of 151/15

3. Students are investigating the motion of a cart that rolls with constant velocity on a horizontal tabletop. The cart is launched from a marked point and moves in a straight line across the table. The students want to determine the magnitude and direction of the cart’s velocity vector as measured in the laboratory reference frame.

Describe an experimental procedure using the equipment provided to collect data that would allow the students to determine $v_x$ . Include any steps necessary to reduce experimental uncertainty.

Describe how the data collected in part A could be graphed and how that graph would be analyzed to determine $v_x$ .

t (s)	x (m)
0.00	0.12
0.20	0.29
0.40	0.45
0.60	0.61
0.80	0.77

The students place the origin at one corner of the grid and perform one trial. From the overhead video, they record the cart’s x-position $x$ at several times $t$ after the cart begins moving. The data are shown in Table 1.

The students correctly determine that the relationship between $x$ and $t$ for this trial is $x = x_0 + v_x t$ , where $x_0$ is the x-position at $t = 0$ .

The students create a graph with $t$ plotted on the horizontal axis.

Indicate what measured or calculated quantity could be plotted on the vertical axis to yield a linear graph whose slope can be used to calculate an experimental value for $v_x$ .

Vertical axis: Horizontal axis: $t$

ii.

On the blank grid provided, create a graph of the quantities indicated in part C(i) that can be used to determine $v_x$ .

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Use Table 2 to record the data points or calculated quantities that you will plot.

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Clearly label the vertical axis, including units as appropriate.

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Plot the points you recorded in Table 2.

iii.

Draw a straight best-fit line for the data graphed in part C(ii).

Figure 1. Top-down laboratory setup for measuring the cart’s horizontal position x as a function of time t using an overhead camera and a taped coordinate grid on the tabletop.

Figure 2. Two inertial reference frames: laboratory frame S and moving-walkway frame S′ translating in the +x direction with speed u relative to S.

Using the best-fit line that you drew in part C(iii), calculate the magnitude of the cart’s velocity as measured by the observer on the moving walkway, $|\vec{v'}|$ . Express your answer in $\text{m/s}$ . A moving walkway is set up so that an observer rides along the +x direction with constant speed $u = 0.30\ \text{m/s}$ relative to the laboratory frame S, as shown in Figure 2. The cart’s velocity in the lab frame is found from the graph in part C to have components $v_x$ and $v_y = 0.45\ \text{m/s}$ .

Assume both frames are inertial and that the walkway’s motion is entirely along the +x direction.