`a(t) = sin(t) + 3cos(t), s(0) = 0, v(0) = 2` A particle is moving with the given data. Find the position of the particle.

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Chapter 4, Review - Problem 74 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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hkj1385 | (Level 1) Assistant Educator

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`a(t) = sin(t) + 3cos(t)`

`v(t) = -cos(t) + 3sin(t) + a`

`Now, v(0) = 2`

`Thus, 2 = -cos(0)+3sin(0)+a`

`or, 2 = -1 + 0 + a`

`or., a = 3`

`Now, v(t) = -cos(t) + 3sin(t) + 3`

`Thus, s(t) = -sin(t) - 3cos(t) + 3t + b`

`Now, s(0) = 0`

`Thus, 0 = -sin(0) - 3cos(0) + 0 + b`

`or, b = 3`

`Hence , s(t) = -sin(t) -cos(t) + 3t + 3`

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