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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

`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`

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial