---
title: "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  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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url: "https://nerd-notes.com/ubq/123983/"
date_modified: "2026-09-28T13:29:54+00:00"
---

# 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 \(0 < t  v_B(t)\). 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?

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?

![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.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602194-mR9vUz.jpg)

- **A.** Vehicle A and vehicle B are at the same position because the intersection of their velocity-time curves at \(t = T\) indicates that vehicle B has caught up to vehicle A.
- **B.** Vehicle A is ahead of vehicle B because the definite integral \(\int_0^T v_A(t)\,dt\) is greater than the definite integral \(\int_0^T v_B(t)\,dt\).
- **C.** Vehicle B is ahead of vehicle A because the derivative \(\dfrac{dv_B}{dt}\) is greater than \(\dfrac{dv_A}{dt}\) at \(t = T\), indicating that vehicle B has achieved a larger displacement.
- **D.** Vehicle A is ahead of vehicle B because vehicle A has experienced a greater average acceleration over the time interval \(0 \le t \le T\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123983/*