what would the displacement formula be if an object has constant acceleration and initial velocity
Denote the constant acceleration as `a` and the initial velocity as `V_0.` Then the velocity of object as a function of time t will be
(the velocity is changed constantly).
Integrating this over t we obtain that the position S is equal to
where `S_0` is the initial position. The displacement from `S_0` will be
`V_0*t+(a*t^2)/2.` This is the answer. `V_0` and `a` generally are vectors. If they have the same direction, the answer also true for their magnitudes.