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The velocity of a particle moving along the x-axis is v(t) = t^2 + 2t + 1, with t measured in minutes and v(t) measured in feet...Asked by xinyan
The velocity of a particle moving along the x-axis is v(t) = cos(2t), with t measured in minutes and v(t) measured in feet per minute. To the nearest foot find the total distance travelled by the particle from t = 0 to t = π minutes.
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Answered by
oobleck
∫[0,π] cos(2t) dt = 0
How can this be? It is because the integral gives the displacement after π minutes, rather than the distance traveled. What you want to integrate is speed, rather than velocity.
∫[0,π] |cos(2t)| dt = 2
or, due to the symmetry of the graph, you could alo just take
4∫[0,π/4] cos(2t) dt = 2
How can this be? It is because the integral gives the displacement after π minutes, rather than the distance traveled. What you want to integrate is speed, rather than velocity.
∫[0,π] |cos(2t)| dt = 2
or, due to the symmetry of the graph, you could alo just take
4∫[0,π/4] cos(2t) dt = 2
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