APFIVE Particle Motion and Total Distance
At time $$t$$, $$0 < t < 2$$, the velocity of a particle moving along the $$x$$-axis is given by $$v(t) = t \sin(t^3)$$. Let $$t = b$$ be the time at which the particle changes direction from moving left to moving right. What is the total distance traveled by the particle during the time interval $$0 < t < b$$?
A
$$0.212$$
B
$$1.011$$
C
$$0.612$$
D
$$1.208$$
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