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

Textbook Question

Chapter 4, 4.9 - Problem 59 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`v(t)=sin(t)-cos(t)`

`v(t)=s'(t)`

`s(t)=intv(t)dt`

`s(t)=int(sin(t)-cos(t))dt`

`s(t)=-cos(t)-sin(t)+C`

Let's find the constant C , given s(0)=0

`s(0)=0=-cos(0)-sin(0)+C`  

`0=-1-0+C`

`C=1`

`:.`  position of the particle is given by `s(t)=-cos(t)-sin(t)+1`

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