Aparticle moves along the x-axis so that at any time t, t ≥ 0, its acceleration is a(t) = -4sin(2t). if the velocity of the particle at t = 0 is v(0) = 7 and its position at t = 0 is x(0) = 0, then its position at time t is x(t) = ?

a. sin(2t) + 5t
b. sin(2t) + 7t
c. sin(2t) + 9t
d. 16sin(2t) + 7t

The velocity of the particle is given by

Since and , we get

Similarly, the position function is obtained via

We know and we're told that , so

making the answer A.

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your answer is 125y5