Question

in addition to speed what else should we known to predict the position of a moving body

Answer 1

To predict the instantaneous position s (t) of a body at any time instant t, we need to know 
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1) the time instant t
2) s(0) its initial position at t = 0:  s(0)
3) v(t) the instantaneous speed v at every instant of the object.
4) the direction of velocity at every instant of the object:  

(3) and (4) combined is the instantaneous velocity vector.

Answer 2

we should know the direction the body travels.
according to equation s=ut=0.5at^2
to ditermine directions we need to find the velocity (initial and final),accleration and time.