A small bar magnet is released from rest and falls under gravity...

When the magnet falls, the changing magnetic flux induces eddy currents in the copper tube.

According to Lenz's law, these induced currents produce a magnetic force that opposes the downward motion of the magnet. The magnitude of this opposing force is proportional to the velocity of the magnet ($F_{m} = kv$).

The net downward force on the magnet is $F_{net} = mg - kv$, which means the acceleration is $a = g - \dfrac{k}{m}v$.

As the velocity $v$ increases, the downward acceleration $a$ (which is the slope of the $v-t$ graph) decreases. Eventually, the acceleration becomes zero when $v = \dfrac{mg}{k}$, and the magnet continues to fall with this constant terminal velocity.

Thus, the $v-t$ graph is a curve starting from the origin with a continuously decreasing positive slope, eventually approaching a horizontal asymptote.

Answer: A curve starting from the origin, whose slope continuously decreases to zero as the velocity approaches a constant maximum value.