At $t=0$ the particle is at $y=30$, and as $t\rightarrow\infty$ the particle tends to $y=35$.

At $t=0$ the particle has negative velocity $v=-5$. If it were to carry on at this velocity it would sail on past the origin and head into the negative $y$ direction. It does not do this - its speed decreases as it approaches the origin and it eventually comes to a rest at $y=0$ in the limit $t\rightarrow\infty$. In order for this to happen it must be accelerating in the positive $y$ direction so that it's speed towards the negative direction decreases with time.