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Mathematics 32 Online
OpenStudy (imnotarobot5):

A particle is moving along the x-axis so that its position at t ≥ 0 is given by s(t) = (t)In(5t). Find the acceleration of the particle when the velocity is first zero.

OpenStudy (danjs):

find the first two derivatives s(t) = t*ln(5t) v(t) = s'(t) a(t) = v'(t)=s''(t)

OpenStudy (518nad):

go ahead take the derivatives

OpenStudy (imnotarobot5):

s'(t) = ln5t + 1 ? s''(t) = 5/5t

OpenStudy (danjs):

right, the functions for position, velocity, and acceleration s(t)=t*ln(5t) v(t)=ln(5t)+1 a(t)=1/t Find a(t) when v(t)=0

OpenStudy (imnotarobot5):

where does a(t) come from?

OpenStudy (danjs):

the second derivative a(t)=s''(t), position---velocity---acceleration

OpenStudy (danjs):

it says Find the acceleration of the particle when the velocity is first zero When is the velocity first zero? set v(t) = 0 and solve for time t. v(t)=ln(5t)+1 = 0 ln(5t) =-1 t = e^-1 / 5

OpenStudy (danjs):

The velocity is zero at that time t... so the acceleration at that time is \[\large a(\frac{ e^{-1} }{ 5 })=\frac{ 1 }{ e^{-1}/5 }=5*e\]

OpenStudy (danjs):

approx... 13.59

OpenStudy (imnotarobot5):

Ahh i get it, i forgot to reduce it. Thank you!

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