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The slope of a distance time graph is a measure of the rate of change in the distance of the object from a fixed reference point along the radial direction. If there were no acceleration in that direction then the radial velocity would be the same so that the graph would be a straight line. However, a curve indicates not only the the distance is changing with time, but that the rate of change is also changing. That is, the radial velocity is changing and that is indicative of radial acceleration.

The word "radial" appear many times in the above paragraph. This is to emphasise that distance time graphs look only at the motion of an object in the direction towards or away from the reference point. Any motion is a transverse direction is ignored. Thus, a line with a constant gradient (slope) does not indicate that there is no acceleration but that any acceleration is in the direction at right angles to the reference direction.

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7y ago
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12y ago

an increasing distance is traveled during each unit of time

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7y ago

You can look at it the other way... if you have constant acceleration, that will be graphed as a straight line.

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Q: Why does a curve on a distance-time graph indicate acceleration?
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an increasing distance is traveled during each unit of time


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