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.

Answer 1

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.