Trisarahtops
  • Trisarahtops
A particle moves along the x-axis with position function s(t) = e^cos(x). How many times in the interval [0, 2π] is the velocity equal to 0? 1 2 3 More than 3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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baru
  • baru
do you know how to differentiate?
Trisarahtops
  • Trisarahtops
I think so yeah
baru
  • baru
s(t) is the function for postition. the derivative of s(t) with respect to time is velocity. i'm sure the question is actually e^cos(t) so can you find V=ds/dt ?

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Trisarahtops
  • Trisarahtops
no it is s(t) = ecos(x). So do i start with ln e^(cos x)
Trisarahtops
  • Trisarahtops
*s(t) = e^cos(x)*
baru
  • baru
the question makes sense only if s(t)=e^cos(t)
Trisarahtops
  • Trisarahtops
oh but my problem has x not t....would that matter or can we continue?
baru
  • baru
we'll it matters. buts lets just consider it a mistake in the text book, and change the question to s(t)=e^cos(t)
baru
  • baru
what you should do is differentiate s(t) with respect to t
Trisarahtops
  • Trisarahtops
so I would have -e^cos(x) sin(x)
baru
  • baru
yes. except its not x its t. now we know that the whole expression is zero when ever sin(t) is zero. do you know when sin( ) is zero in the intervall [0,2pi] ?
Trisarahtops
  • Trisarahtops
does this have to do with the unit circle
baru
  • baru
yes
Trisarahtops
  • Trisarahtops
i don't know ;/
baru
  • baru
\(sin(n\pi) \) =0 where n is any integer so in the interval [0,2pi] we have sin(0), sin(pi) and sin (2pi) (n=0,1 and) 3 times (at t=0 , pi and 2pi)
Trisarahtops
  • Trisarahtops
ooohh okay i see. Thank you :D

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