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A particle moving along the x axis so that it’s position at t is greater than or equal to 0 is given by s(t)=(t)ln(3t). Find the acceleration of the particle when the velocity is first zero.

User Tad Dallas
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1 Answer

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We are given

equation of position


s(t)=(t)ln(3t)

Calculation of velocity:

we can find derivative


s'(t)=1*ln(3t)+t*(3)/(3t)


s'(t)=ln(3t)+1

so, velocity is


v(t)=ln(3t)+1

now, we can set it to 0

and then we can solve for t


v(t)=ln(3t)+1=0


t=(1)/(3e)

Calculation of acceleration:

we can find derivative again


v'(t)=(3)/(3t) +0


v'(t)=(1)/(t)

so, acceleration is


a(t)=(1)/(t)

now, we can plug value of t


a((1)/(3e))=(1)/((1)/(3e))


a((1)/(3e))=3e..................Answer


User Intcreator
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