If two automobiles have the same velocity, do they have the same acceleration?

Not at all.

Examples:

-- They could be on the same road, driving in the same direction.
Still, one may be slowing down while the other one is speeding up.
Then, their accelerations have opposite signs, and may have different
magnitudes, but there may very well be an instant when their velocities
are equal.

-- They may both have the same steady speed, but one is on a straight
road while the other one is on a circular track.  At the instant when both
are facing in the same direction, their velocities are equal, although the
first one has no acceleration at all and the second one has a constant
centripetal acceleration.

The best description is: . nobody has any idea what q is.