The distance-time graph of a body is shown below. The speed-time graph of the body is

Question

BlackTom AI · Accepted Answer

To connect the distance–time graph to a speed–time graph, recall that the slope of the distance–time curve at any point equals the instantaneous speed.

Option A: The speed–time graph would show a quick rise to a peak and then a fall back to zero, forming a triangular shape entirely in the positive speed region. If the distance–time graph had a corresponding symmetrical triangular slope, this would imply a speed that rises and then falls quickly in a symmetric way, which does not match the smooth curved distance–time graph shown (whose slope gradually decreases rather than peaking and decreasing instantaneously). Therefore, A does not fit.

Option B: This option depicts speed increasing and then leveling off at a nonzero speed. A distance–time graph with a speed that increases and then stays constant would produce a distance–time curve with a slope that becomes constant after some time, not the curved, decelerating shape shown. Since the given distance–time graph shows a decreasing slope toward the end (speed decreasing to zero), B is inconsistent.

Option C: Here the speed–time graph shows a constant speed from t = 0 to t = 2 s, followed by a linear decline to zero at t = 4 s. This matches a distance–time curve that starts with a steep slope, then the slope gradually decreases and eventually flattens as t approaches 4 s. The concave-down, increasing distance with diminishing slope aligns with a constant speed briefly and then a deceleration to rest, which is exactly what option C represents.

Option D: This graph would indicate an abrupt change or a discontinuity in speed (e.g., a sudden jump or a sudden stop) that would produce a distance–time relationship with sharp corners not seen in the smooth curve provided. Since the distance–time graph is smooth and gradually decelerates, D does not correspond.

In summary, the distance–time graph’s decreasing slope toward the end implies the speed is constant for a while and then decreases linearly to zero. The only option that reproduces this behavior in the speed–time domain is C.

The distance-time graph of a body is shown below. The speed-time graph of the body is Single choice

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