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AP Physics C: Mechanics
1.3 Representing Motion
1.2 Displacement, Velocity, and Acceleration
IntermediateMCQGraphicalMathematical14k
A Cartesian graph with a horizontal time axis labeled \(t\) and a vertical position axis labeled \(x\). The horizontal axis has five tick marks labeled \(0\), \(T/4\), \(T/2\), \(3T/4\), and \(T\). The vertical axis has three tick marks labeled \(+x_0\), \(0\), and \(-x_0\). A single solid curve represents a smooth cosine wave starting at \((0, x_0)\), crossing the horizontal axis downward at \(t = T/4\), reaching a smooth minimum at \((T/2, -x_0)\), crossing the horizontal axis upward at \(t = 3T/4\), and reaching a smooth maximum at \((T, x_0)\). Dashed horizontal guide lines extend from \(+x_0\) and \(-x_0\) across the plot. No other labels, lines, text, or curves appear.
Position versus time graph of the object over one period.
The position \(x\) of an object moving along the \(x\)-axis as a function of time \(t\) is modeled by \(x(t) = x_0 \cos(\omega t)\), where \(x_0\) is a positive constant and \(\omega = \dfrac{2\pi}{T}\). The object's motion over one complete period from \(t = 0\) to \(t = T\) is shown in the graph. Which of the following graphs best represents the acceleration \(a\) of the object as a function of time \(t\) over the same interval?

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