A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is given by a(t) = 6cos(t). At the time t = 0, its position is x = 6.
(a) Find the velocity and position functions for the particle.
(b) Find the values of t for which the particle is at rest.

a. By the fundamental theorem of calculus, the velocity function is

The particle starts at rest, so , and we have

Then the position function is

with , so

b. The particle is at rest whenever ; this happens for

where is any integer.

go hook jvc hgv cj xk jvc 6756

6 hours 48 min

step-by-step explanation:

68÷5=13.6

13.6×30=408min=6 hours 48 min.

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