Velocity must be positive. (discover)

Many students have difficulty in associating a reverse in direction with a change in sign. Some students will insist that, like speed, velocity must be positive.

Same position means same speed. (discover)

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

Leading (following) particle moves at a faster (slower) speed. (discover)

Due to difficulties in differentiating the concepts of position, velocity, and acceleration, students tend to treat particle position as a direct indicator of particle speed. If one particle is in front of another, they will assume that it is traveling at a faster speed.

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.

A positive slope for a negative velocity means the object is speeding up. (discover)

Many student's interpret a positive slope as speeding up (and a negative slope as slowing down) irrespective of the direction (sign) of the velocity.

 

Students plot position and velocity graphs as the path of the particle. (discover)

Students often display difficulty in graphing the motions of particles. They appear to lack the skill of dissociating the motion of the particle from the path that it is taking. Thus they redraw the path of the particle when asked to graph the particle's position or velocity versus time.

Velocity is intrinsic to a particle, and doesn't depend on the observer (i.e. the ground is a preferred observer). (discover)

Many students asked to measure the velocity of a particle in two differently moving reference frames will say that the velocities are the same. Student's familiarity using the ground as a reference frame inhibits their using moving frames when observing physical phenomena.