Deltax = x_0 + v_0 t + 1/2 a t^2

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The Distance Traveled equation, dx= x_0+v_0⋅t+0.5⋅a⋅t^2, calculates the distance traveled (dx) by an object from the origin after a period of time (t), based on its initial distance from the origin (X_o), the objects initial velocity (V_o) and a constant acceleration (a). distance traveled a.k.a. displacement

dx = x_0 + v_0*t + 0.5*a*t^2

Application

A common application for this equation is the travel associated with the free fall of an object under the force of gravity. In the case of Earth's gravity, the constant acceleration is approximately 9.80665 m/s².  Note that this formula does not include other forces such as drag.

Notes

See this video discussing a real use for this equation: