Same velocity means same acceleration for two objects. (discover)

Students have difficulty differentiating the concepts of position, velocity, and acceleration. This results in students assuming that two particles with identical velocities (at an instant) have identical accelerations (similarly, two particles with identical positions (at an instant) have identical speeds).

Larger (smaller) velocity means larger (smaller) acceleration. (discover)

Due to difficulties in differentiating the concepts of position, velocity, and acceleration, students tend to treat particle velocity as a direct indicator of particle acceleration. This difficulty may stem from a misunderstanding of acceleration as the ratio Dv/Dt, or possibly from student's experiences driving a car (pressing the accelerator to go faster).

Zero velocity means zero acceleration. (discover)

Due to difficulties in differentiating the concepts of position, velocity, and acceleration, many students believe that a particle that has no velocity at an instant cannot be accelerating. This difficulty may stem from a misunderstanding of acceleration as the ratio Dv/Dt, and/or a misunderstanding of the time interval Dt.

 

Students fail to see acceleration as the ratio Dv/Dt. (discover)

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.