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If the displacement varies as the cube of time then acceleration is linear in time.
In physics and engineering, the time rate of change of acceleration is called "jerk."
(See related link.)

Here is the math.
1. We are given that the displacement of a particle is proportional to the cube of the time.

We put this statement into the form, d= c * t3.

2. The velocity of an object is the time rate of change of position (displacement).

v=3c*t2

3. The acceleration of an object is the time rate of change of the velocity.

a=6c*t


4. The acceleration is then linear in time and the jerk is, j=6c.

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11y ago
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9y ago

If displacement is directly proportional to the square of time, would have to do with the rate of change of acceleration.

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Q: What is the graph of displacement directly proportional to the cube of time?
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