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A particle starts from rest at the origin and moves along a straight line. Its acceleration is given by \(a(t) = \cos(\frac{\pi}{4}t)\) m/s\(^2\), for \(t \ge 0\).
Find the velocity function \(v(t)\) of the particle.
What is the maximum speed of the particle?
Find the total distance travelled by the particle in the first 4 seconds.
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