Identifying Accelerations from Graphs
Classical Mechanics
Level
2
The below plot shows the positions of four particles undergoing different constant accelerations as a function of time. What is the color of the curve that represents the particle accelerating at the fastest rate?
Red
Gold
Green
Blue
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The green and blue curves are distractions; although the magnitudes of the displacements of both may be larger at any given time, the displacement is clearly growing at a much slower rate than the other two curves, so their accelerations will not be as large.
To note that the red curve represents a larger acceleration than the gold curve, note that the gap between the two curves is closing over time. Although the gap grew briefly because the gold curve started with a nonzero velocity and the red did not, the fact that the red is starting to overtake the gold means that the red is accelerating more quickly; the faster acceleration will win out over time because the acceleration term is quadratic in time.