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

Question

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

bobpursley · Accepted Answer

s=t*ln(5t)=t(lnt+ln5) s'=(lnt+ln5)+t(1/t+0) s"=acceleration=1/t so find time when s'=0 0=(lnt+ln5)+1 ln5t=-1 5t=e^-1 t= 1/5e a(1/5e)=1/t=5e check my work.