What do student responses to the car-truck problems tell us? An investigation into two Force Concept Inventory questions
Abstract
Concept inventories are widely used in Physics Education Research to uncover student misconceptions and measure the effectiveness of instruction. Two questions in the widely used multiple-choice Force Concept Inventory concern a car that is pushing a truck, as the car is accelerating and then when a steady speed has been reached. We investigate the premise that correct answering of these questions is because of good conceptual understanding of Newton's Third Law, by analyzing responses to a modified inventory that randomly offers students multiple-choice or free-text versions of the questions and follows these with questions in which students select the physical principle(s) they used. The results from 674 attempts from students at six universities show a similar pattern of results for multiple-choice and free-text versions, also comparable with Force Concept Inventory results from one of the universities in the preceding five years, but with marked differences relative to early published Force Concept Inventory data. Free-text responses and the law-selection sub-questions can reveal more about conceptual understanding than can be seen in multiple-choice responses alone. For the accelerating system (Question 15), correct responses are usually attributed to Newton's Third Law and incorrect responses are usually attributed to Newton's Second Law. When speed is constant (Question 16), around 90% of responses are correct, but a significant number of these are attributed to Newton's First Law or the Superposition Principle rather than Newton's Third Law, especially pre-instruction. We conclude that students are confusing balanced forces on a single object moving at constant speed with the correct equal-and-opposite interaction pair between two objects, and correct responses to Question 16 may be concealing an underlying misconception.
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BibTeX
@misc{pathak2026what,
title = {{What do student responses to the car-truck problems tell us? An investigation into two Force Concept Inventory questions}},
author = {Ashutosh Kumar Pathak and Mark A. J. Parker and Ross K. Galloway and Andrew J. A. James and Sally E. Jordan and Jonathan Nylk},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01477},
eprint = {2609.01477},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01477},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - What do student responses to the car-truck problems tell us? An investigation into two Force Concept Inventory questions
AU - Ashutosh Kumar Pathak
AU - Mark A. J. Parker
AU - Ross K. Galloway
AU - Andrew J. A. James
AU - Sally E. Jordan
AU - Jonathan Nylk
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01477
UR - https://arxiv.org/abs/2609.01477
AB - Concept inventories are widely used in Physics Education Research to uncover student misconceptions and measure the effectiveness of instruction. Two questions in the widely used multiple-choice Force Concept Inventory concern a car that is pushing a truck, as the car is accelerating and then when a steady speed has been reached. We investigate the premise that correct answering of these questions is because of good conceptual understanding of Newton's Third Law, by analyzing responses to a modified inventory that randomly offers students multiple-choice or free-text versions of the questions and follows these with questions in which students select the physical principle(s) they used. The results from 674 attempts from students at six universities show a similar pattern of results for multiple-choice and free-text versions, also comparable with Force Concept Inventory results from one of the universities in the preceding five years, but with marked differences relative to early published Force Concept Inventory data. Free-text responses and the law-selection sub-questions can reveal more about conceptual understanding than can be seen in multiple-choice responses alone. For the accelerating system (Question 15), correct responses are usually attributed to Newton's Third Law and incorrect responses are usually attributed to Newton's Second Law. When speed is constant (Question 16), around 90% of responses are correct, but a significant number of these are attributed to Newton's First Law or the Superposition Principle rather than Newton's Third Law, especially pre-instruction. We conclude that students are confusing balanced forces on a single object moving at constant speed with the correct equal-and-opposite interaction pair between two objects, and correct responses to Question 16 may be concealing an underlying misconception.
ER -