The initial velocity of particles can be set through different parameters, based on the type of the particle system. If the particle system type is Emitter or Hair, then the following parameters give the particle an initial velocity in the direction of…
The emitter’s surface normals (i.e. let the surface normal give the particle a starting speed).
Let the tangent speed give the particle a starting speed.
Rotates the surface tangent.
Give an initial velocity in the X, Y, and Z axes.
X, Y, Z
The emitter objects movement (i.e. let the object give the particle a starting speed).
Gives the starting speed a random variation. You can use a texture to only change the value, see Controlling Emission, Interaction and Time.