When dealing with higher time derivatives like jerk, how does one find the distance traveled? Can it be calculated by just knowing time?
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9$\begingroup$ Integration, integration, integration.... $\endgroup$– CuriousOneCommented May 3, 2015 at 2:36
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$\begingroup$ You have to solve 3rd order differential equation with initial conditions $\endgroup$– PaulCommented May 3, 2015 at 2:49
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$\begingroup$ Why did someone vote to close this? $\endgroup$– Jimmy360Commented May 3, 2015 at 3:22
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$\begingroup$ I didn't. I think it's a legitimate question, even if jerk doesn't occur in too many problems. $\endgroup$– CuriousOneCommented May 3, 2015 at 4:32
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2 Answers
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Integrate the jerk 3 times then using starting conditions to work out the integration constants.
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Knowing only "jerk" (third derivative of position), you cannot determine the distance traveled.
To get distance traveled (or equivalently, position as a function of time) from jerk, you need to integrate three times. Each integration produces a constant of integration representing an initial value; your final equation looks something like this:
$$p(t) = \iiint j(t) + at^2 + vt + x$$
where "a" is your initial acceleration, "v" is your initial velocity, and "x" is your initial position. "x" doesn't matter for computing distance traveled, but the other two do.
