# what would the displacement formula be if an object has constant acceleration and initial velocity

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Borys Shumyatskiy | Certified Educator

Hello!

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

`V(t)=V_0+a*t`

(the velocity is changed constantly).

Integrating this over t we obtain that the position S is equal to

`S(t)=S_0+V_0*t+(a*t^2)/2,`

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.