Draw the acceleration-time graph given a sinusoidal position-time graph| University Physics

The main graph shows position versus time for a certain object. Which of the graphs below correctly depicts the object’s acceleration?

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ANSWER: Graph D

The given position vs time graph is sinusoidal. This is a variation of the graph of a sine function. The acceleration function is the second derivative of the position-time function. Therefore, the acceleration function should be a variation of the negative sine function. From among the choices, the one that depicts a negative sign function is only graph D.