anonymous
  • anonymous
A particle moves along the x-axis with the velocity given by v(t)=3t/(1+t^2) for t >or equal to 0. When t=0, the particle is at the point (4,0). 1. Determine the maximum velocity for the particle. Justify your answer. 2. Determine the position of the particle at any time t. 3. Find the limit of the velocity as t->infinity. 4. Find the limit of the position as t->infinity.
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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shubhamsrg
  • shubhamsrg
dx = vdt use this..this little thing is supposed to do wonders for you ! :D
anonymous
  • anonymous
Could you explain how that formula works please?
shubhamsrg
  • shubhamsrg
have you studied integration ?

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anonymous
  • anonymous
Just started learning it. It's not my best subject. xD
anonymous
  • anonymous
the definition of velocity is v=dx/dt
anonymous
  • anonymous
1. a(t) = 3(1-t^2)/(1+t^2)^2 max v at a=0, or t=1 v(1) = 3/2 2. x(t) = 3/2 log(1+t^2)+C at t=0, x=4, so 4 = 3/2 log(1+0) + C C = 4 x(t) = 3/2 log(1+t^2) + 4 3. v(t) → 0 as t→∞ 4. x(t) → ∞ that's what I've got so far. Does that make sense?
anonymous
  • anonymous
@sauravshakya
shubhamsrg
  • shubhamsrg
you sure differentiated right in the 1st part.. rest all seem perfect! :)
anonymous
  • anonymous
At least someone agrees with it so far.
shubhamsrg
  • shubhamsrg
i missed a question mark there :P i meant you sure differentiated right in the 1st part ???? :D cause i see that wrong..please confirm..
shubhamsrg
  • shubhamsrg
ohh wait//thats -t^2 // sorry sorry..thats correct..
shubhamsrg
  • shubhamsrg
my apologies! :P
anonymous
  • anonymous
Yeah I just checked. oh well haha
anonymous
  • anonymous
Could somebody please check this to make sure it makes sense? 1. dv/dt = [(1+t^2)(3) - 3t(2t)] / (t^2+1)^2 =[3 t^2 + 3 - 6 t^2 ] /(t^2+1)^2 zero when t= 1 (since t always >/=0) so the max v is at t = 1 then at t = 1 v(1) = 3/2 2. x(t) = 3/2 log(1+t^2)+C at t=0, x=4, so 4 = 3/2 log(1+0) + C C = 4 x(t) = 3/2 log(1+t^2) + 4 3. as t --> oo, v--> 3t/t^2 = 3/t = 0 4. as t -->oo, x --> (3/2)t^2 = oo

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