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AP Physics C: Mechanics
1.3 Representing Motion
1.2 Displacement, Velocity, and Acceleration
AdvancedMCQMathematicalConceptual17.8k
A Cartesian graph with a horizontal axis labeled t and a vertical axis labeled v, intersecting at the origin (0, 0). The axes have bare lines without gridlines. A solid curve representing vehicle A starts at the origin (0, 0), curves upward with decreasing slope, and reaches the coordinate point (T, v_0), continuing past it with a smaller positive slope. A dashed curve representing vehicle B starts at the origin (0, 0), curves upward with increasing slope, lies entirely below the solid curve across the interval 0 < t < T, and intersects the solid curve at the single point (T, v_0), continuing upward with a steeper positive slope for t > T. A vertical dashed guideline drops from (T, v_0) to a tick labeled T on the horizontal axis, and a horizontal dashed guideline extends from (T, v_0) to a tick labeled v_0 on the vertical axis. A text label v_A is placed adjacent to the solid curve and a text label v_B is placed adjacent to the dashed curve. No other labels, lines, text, or axes appear.
Velocity versus time for vehicles A and B.
Two vehicles, A and B, travel in the positive x-direction along parallel straight tracks, both starting from rest at position \(x = 0\) at time \(t = 0\). For the time interval \(0 < t < T\), the velocity of vehicle A is strictly greater than the velocity of vehicle B, such that \(v_A(t) > v_B(t)\). At time \(t = T\), both vehicles have the same velocity \(v_A(T) = v_B(T) = v_0\), and for \(t > T\), vehicle B has a greater velocity than vehicle A. Which of the following statements correctly compares the positions of the two vehicles at time \(t = T\) and provides the correct physical justification?

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