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Integrating the definitions of acceleration and velocity for the special case that acceleration is constant leads to four expressions that are commonly encountered in descriptions of motion with constant acceleration:

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{center}{latex}\begin{large}\[ v_{f} = v_{i} + a(t_{f}-t_{i})\]\[x_{f} = x_{i} + \frac{1}{2}(v_{f}+v_{i})(t_{f}-t_{i})\]\[x_{f}=x_{i}+v_{i}(t_{f}-t_{i})+\frac{1}{2}a(t_{f}-t_{i})^{2}\]\end{large}{latex}{center}

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