Descriptions of Common Student Difficulties with Problem Solving
Many students think that two blocks connected by a (continuously) taught inextensible string can move at different velocities and/or accelerations, even though the distance between the blocks remains the same.
Most students can determine the formulae needed, from the data given in many of the problems listed in introductory texts, without having an understanding of the physical situation involved.
Some student's view acceleration as the velocity that an object has during the time interval in question. Other students who realize that acceleration is brought about by a change in velocity, don't directly relate the corresponding time interval with that change. Still other students associate acceleration as the change in velocity over a distance traveled (Dv/Dx), rather than the time taken for the change.
When given a problem involving two quantities, in which one quantity increases, while the second quantity decreases, students will often claim that the net result in the product (or other similar mathematical function) of the two quantities is unchanged, since the increase of one compensates for the decrease in the other.