Find the total distance traveled by a particle given its velocity function Question A particle travels according to the velocity function v(t) = -3t + 9 m/sec. What is the total distance traveled by the particle over the time interval [0, 4]? Enter your answer as an exact fraction if necessary and do not include units in your answer.
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This is done by integrating the velocity function over this interval. The integral of v(t) from 0 to 4 is ∫v(t) dt from 0 to 4 = ∫(3t + 9) dt from 0 to 4. This integral can be computed as [1.5t^2 + 9t] from 0 to 4 = (1.5*4^2 + 9*4) - (1.5*0^2 + 9*0) = 24 + 36 = Show more…
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