Something I only grappled recently in Physics is that if you run a 400m race on a standard track your velocity is...
0!
I'm tired and not too sure of myself, but surely only your initial and final velocity would be 0. Given that vectors have both magnitude and direction, if you run say 100 of the 400m in say, 10 seconds, then your displacement in the x direction (at 0 degrees) is given by;
displacement = rcos(theta) where r is the magnitude and equal to, by the Pythagorean Law the square root of (x^2 + y^2)
Since you've moved 100 in the x direction and effectively 0 in the y direction, your magnitude is 100... and cos(0) = 1.
so your displacement is infact 100m from its original starting point in a direction of 0 degrees. This'll be used later.
From here, you have to go from acceleration and integrate
So, assuming your acceleration at any time has a magnitude of a (sure it's constant, deal with it.)
acceleration in the x direction = acos(0)
= a
since acceleration is dv/dt
velocity in x direction = at + C where c is the integration constant and effectively your initial velocity which is equal to 0, unless you get a running start.
v(x) = at.
Since velocity is given by dx/dt
x = 1/2at^2 + C where C is your initial displacement = 0
so, you rewrite this as
x = 1/2(v)t
100m = 1/2*v*t
1/2v = 100/t
v = 2*(100/10)
v = 20m/s at the 100m mark moving in a direction of 0 degrees from the initial point.
So there. by my reasoning at 10 at night your velocity is not always 0. Your overall SPEED however is infact 0 since the speed, or magnitude of the velocity is given by distance/time.. so you've effectively travelled 0m over a given time.. and therefore have a velocity of 0.
Once again feel free to say if i'm wrong.
I'm going to bed
goodddnight farkin/rotorburn.
Edit: also I have no idea if what i've said is relevant to anything you were previously talking about, I just grabbed onto the your velocity being zero thing.