---
title: "A motion sensor records the position x of a cart moving along a straight track at regular 1.0 s intervals, as shown in the data table.  | Time t (s) | Position x (m) | |—|—| | 0.0 | 0.10 | | 1.0 | 0.50 | | 2.0 | 1.50 | | 3.0 | 3.30 | | 4.0 | 6.10 |  Using the average velocity across adjacent intervals to estimate the instantaneous acceleration, which row correctly identifies the estimated accelerations of the cart at t = 1.0 s and t = 3.0 s, and states the effect on these calculated values if the sensor had an uncorrected calibration offset of +0.15 m for all position measurements?"
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url: "https://nerd-notes.com/ubq/120512/"
date_modified: "2026-08-23T04:39:23+00:00"
---

# A motion sensor records the position x of a cart moving along a straight track at regular 1.0 s intervals, as shown in the data table.

| Time t (s) | Position x (m) |
|—|—|
| 0.0 | 0.10 |
| 1.0 | 0.50 |
| 2.0 | 1.50 |
| 3.0 | 3.30 |
| 4.0 | 6.10 |

Using the average velocity across adjacent intervals to estimate the instantaneous acceleration, which row correctly identifies the estimated accelerations of the cart at t = 1.0 s and t = 3.0 s, and states the effect on these calculated values if the sensor had an uncorrected calibration offset of +0.15 m for all position measurements?

A motion sensor records the position x of a cart moving along a straight track at regular 1.0 s intervals, as shown in the data table.

| Time t (s) | Position x (m) |
|---|---|
| 0.0 | 0.10 |
| 1.0 | 0.50 |
| 2.0 | 1.50 |
| 3.0 | 3.30 |
| 4.0 | 6.10 |

Using the average velocity across adjacent intervals to estimate the instantaneous acceleration, which row correctly identifies the estimated accelerations of the cart at t = 1.0 s and t = 3.0 s, and states the effect on these calculated values if the sensor had an uncorrected calibration offset of +0.15 m for all position measurements?

- **A.** | Estimated a(1.0 s) | Estimated a(3.0 s) | Effect of +0.15 m Offset | |---|---|---| | \(0.30\text{ m/s}^2\) | \(0.50\text{ m/s}^2\) | No effect |
- **B.** | Estimated a(1.0 s) | Estimated a(3.0 s) | Effect of +0.15 m Offset | |---|---|---| | \(0.60\text{ m/s}^2\) | \(1.00\text{ m/s}^2\) | No effect |
- **C.** | Estimated a(1.0 s) | Estimated a(3.0 s) | Effect of +0.15 m Offset | |---|---|---| | \(0.60\text{ m/s}^2\) | \(1.00\text{ m/s}^2\) | Both values increase |
- **D.** | Estimated a(1.0 s) | Estimated a(3.0 s) | Effect of +0.15 m Offset | |---|---|---| | \(0.80\text{ m/s}^2\) | \(0.71\text{ m/s}^2\) | Both values increase |

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120512/*