tmagloire1
  • tmagloire1
A particle is moving along the x-axis so that its position at t ≥ 0 is given by s(t) = (t)In(2t). Find the acceleration of the particle when the velocity is first zero. 2e^2 2e e None of these
Mathematics
chestercat
  • chestercat
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Vocaloid
  • Vocaloid
well, we can find the derivative of position to get velocity, then we can take the derivative of velocity to get acceleration do you know how to find the derivative of t*ln(2t)? we'll be using the product rule
tmagloire1
  • tmagloire1
@Vocaloid log(2t)+1
Vocaloid
  • Vocaloid
almost, ln(2t) + 1

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tmagloire1
  • tmagloire1
oops i meant ln xD
Vocaloid
  • Vocaloid
no prob, now all we need to do is take the derivative of ln(2t). can you do that?
tmagloire1
  • tmagloire1
So the next derivative is 1/t
Vocaloid
  • Vocaloid
yup! our last step is to figure out what to plug in for t the problem wants to find the acceleration when the velocity is 0, so we go back to our velocity equation and set it equal to 0, then solve for t ln(2t) + 1 = 0 solve for t
tmagloire1
  • tmagloire1
i got 1/2e
Vocaloid
  • Vocaloid
right, t = 1/(2e), now we plug that back into our acceleration equation 1/t = 1/(1/(2e) = 1/(0.5e^-1) = 2e
tmagloire1
  • tmagloire1
Thank you so much for the help!

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