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

Question

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

vocaloid · Answer

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 · Answer

@Vocaloid log(2t)+1

vocaloid · Answer

almost, ln(2t) + 1

tmagloire1 · Answer

oops i meant ln xD

vocaloid · Answer

no prob, now all we need to do is take the derivative of ln(2t). can you do that?

tmagloire1 · Answer

So the next derivative is 1/t

vocaloid · Answer

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 · Answer

i got 1/2e

vocaloid · Answer

right, t = 1/(2e), now we plug that back into our acceleration equation

1/t = 1/(1/(2e) = 1/(0.5e^-1) = 2e

tmagloire1 · Answer

Thank you so much for the help!