For an object experiencing constant acceleration, the expression for position as a function of time is (x(t)=x_{mathrm{i}}+v_{x,
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For an object experiencing constant acceleration, the expression for position as a function of time is \(x(t)=x_{\mathrm{i}}+v_{x, \mathrm{i}} t+\frac{1}{2} a_{x} t^{2}\). Explain, in terms of the area under the \(v(t)\) curve for the object, why the acceleration term includes the factor \(\frac{1}{2}\).
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