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title: "Observer \\(S\\) is at rest on the ground in an inertial reference frame. Observer \\(S’\\) is inside a vehicle that travels along a straight, horizontal track with a constant acceleration of magnitude \\(a_0\\) directed to the right relative to the ground. At \\(t = 0\\), a small object is dropped from rest relative to Observer \\(S\\) and falls vertically with negligible air resistance. Which of the following statements correctly describes the horizontal component of the object’s acceleration as measured by Observer \\(S’\\) and provides the correct justification?"
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url: "https://nerd-notes.com/ubq/120468/"
date_modified: "2026-08-23T04:38:57+00:00"
---

# Observer \(S\) is at rest on the ground in an inertial reference frame. Observer \(S’\) is inside a vehicle that travels along a straight, horizontal track with a constant acceleration of magnitude \(a_0\) directed to the right relative to the ground. At \(t = 0\), a small object is dropped from rest relative to Observer \(S\) and falls vertically with negligible air resistance. Which of the following statements correctly describes the horizontal component of the object’s acceleration as measured by Observer \(S’\) and provides the correct justification?

Observer \(S\) is at rest on the ground in an inertial reference frame. Observer \(S'\) is inside a vehicle that travels along a straight, horizontal track with a constant acceleration of magnitude \(a_0\) directed to the right relative to the ground. At \(t = 0\), a small object is dropped from rest relative to Observer \(S\) and falls vertically with negligible air resistance. Which of the following statements correctly describes the horizontal component of the object's acceleration as measured by Observer \(S'\) and provides the correct justification?

- **A.** The horizontal acceleration is directed to the left with magnitude \(a_0\) because the acceleration of an object relative to a moving frame equals its acceleration in the inertial frame minus the acceleration of the moving frame relative to the inertial frame.
- **B.** The horizontal acceleration is directed to the right with magnitude \(a_0\) because the acceleration of an object relative to a moving frame equals the sum of its acceleration in the inertial frame and the acceleration of the moving frame relative to the inertial frame.
- **C.** The horizontal acceleration is equal to zero because no net horizontal force acts on the object, and acceleration is an invariant quantity across all reference frames.
- **D.** The horizontal acceleration is directed to the left with a magnitude that increases linearly with time because the horizontal speed of Observer \(S'\) increases at a constant rate relative to the ground.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120468/*