Energy in motion?

Question

The position of a particle is given by x = (6 cm) cos 7piT, where T is in seconds.

(a) Find the maximum speed.

(b) Find the maximum acceleration of the particle.

(c) What is the first time that the particle is at x = 0 and moving to the right?

Answer 1

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a) velocity is the first time derivative of position: dx/dt, so d/dt(6cos[7pi t]) = -42pi sin(7pi t)

b) acceleration is the second time derivative of position: d^2x/dt^2, so do the derivative of part a) = -294 pi^2 cos (7 pi t)