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tmagloire1
 one year ago
A particle is moving along the xaxis 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
tmagloire1
 one year ago
A particle is moving along the xaxis 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

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Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1well, 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
 one year ago
Best ResponseYou've already chosen the best response.0@Vocaloid log(2t)+1

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1no prob, now all we need to do is take the derivative of ln(2t). can you do that?

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0So the next derivative is 1/t

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1yup! 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

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1right, t = 1/(2e), now we plug that back into our acceleration equation 1/t = 1/(1/(2e) = 1/(0.5e^1) = 2e

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much for the help!
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