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

1 Answer

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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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.