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title: "An object moves along the x-axis. The graph shows the position x of the object as a function of time t over the interval from t = 0 to t = t_4, with an inflection point occurring at t = t_2. Which of the following statements correctly describes the motion of the object?"
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url: "https://nerd-notes.com/ubq/120477/"
date_modified: "2026-08-23T04:39:03+00:00"
---

# An object moves along the x-axis. The graph shows the position x of the object as a function of time t over the interval from t = 0 to t = t_4, with an inflection point occurring at t = t_2. Which of the following statements correctly describes the motion of the object?

An object moves along the x-axis. The graph shows the position x of the object as a function of time t over the interval from t = 0 to t = t_4, with an inflection point occurring at t = t_2. Which of the following statements correctly describes the motion of the object?

![A 2D line graph with a horizontal axis labeled t and a vertical axis labeled x. The origin is at (0,0). A single continuous solid curve begins at the origin with a positive slope, curves downward to reach a smooth local maximum at t_1, decreases through an inflection point at t_2 where the slope is most steeply negative, flattens out to reach a smooth local minimum at t_3, and curves upward with increasing positive slope through t_4. Vertical dashed lines drop from the curve at times t_1, t_2, t_3, and t_4 to tick marks labeled t_1, t_2, t_3, and t_4 on the horizontal axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459942-qv78F1.jpg)

- **A.** On the time interval \(t_2 < t < t_3\), the acceleration of the object is positive while its speed is decreasing.
- **B.** On the time interval \(t_1 < t < t_2\), the object is slowing down because its position is decreasing.
- **C.** At time \(t = t_2\), the velocity of the object is zero because the graph has a point of inflection.
- **D.** On the time interval \(0 < t < t_1\), the velocity and acceleration of the object are both directed in the positive \(x\)-direction.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120477/*