Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time (t), find the body's position at time (t). a=16 cos4t, v(0)=2, s(0)=5 or see attachment.

s = - 4 cos 4t + 2t + 6.

Explanation:

a = dv/dt = 16 cos 4t ,

dv = 16 cos 4t dt

integrating on both sides

v = 16 x sin 4t /4 + c

    = 4 sin 4t + c

when t = 0 , v = 2

2 = 0 + c

c = 2

v = 4 sin 4t + 2

ds/dt = 4 sin 4t + 2

ds = ( 4 sin 4t + 2) dt

integrating on both sides

s = - 4 cos 4t/4 + 2t + k

    = - cos 4t + 2t + k

when t = 0 s = 5

5 =  -1 + 0 + k

k = 6

s = - 4 cos 4t + 2t + 6.

Ans.

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