Speed = (distance traveled) / (time to travel the distance).
Strange as it may seem, 'velocity' is completely different.
Velocity doesn't involve the total distance traveled at all.
Instead, 'velocity' is based on 'displacement' ... the distance
between the start-point and end-point, regardless of the route
taken to get there. So the displacement in driving once around
any closed path is zero, because you end up where you started.
Velocity =
(displacement during some time)
divided by
(time for the displacement)
AND the direction from the start-point to the end-point.
For the guy who drove 15 km to his destination in 10 min, and then
back to his starting point in 5 min, (assuming he returned by way of
the same 15-km route):
Speed = (15km + 15km) / (10min + 5min) = (30/15) (km/min)
= 2 km/min.
Velocity = (end location - start position) / (15 min) = Zero .
