How do I interpret/make sense of $\frac{d\theta}{dt}$ in physics’ language? Here’s a question from my textbook. It’s a simple question that involves a little bit of calculus. I was able to solve it. But what I don’t understand is, I could not fully understand the final result. How to comprehend $\frac{d\theta}{dt}$ physically? 
I understand that the angle $\theta$ is changing with time $t$, as speed of the boy increases at the rate of ($2$$\frac{m}{s^2}$). After a long time has passed, $\theta$ will approach $90°$. I understand this part. But the final result that I got $\frac{d\theta}{dt}$ = $\frac{1}{1+t^2}$ 
This is what I am unable to absorb in physics’ language. Does it mean the rate of change of $\theta$ is not constant? Or does it mean something else? How do I interpret/make sense of the final result that I got? Thank you
*This is not a homework question. Because it’s not that I need help solving this. I just want to interpret/make sense of the final result that I got, in the language of physics. And I posted the picture so that it makes it easier for someone on here to help me, to understand what exactly I am trying to ask.

 A: The rate of change of the angle $\theta$ is not constant. You can reach this conclusion intuitively by thinking about what it means for the angle to approach 90$^\circ$ after a long time. This means that the rate of change must decrease as the angle approaches 90$^\circ$ so that the angle never reaches beyond this; otherwise, the boy's umbrella would be pointing downwards, which doesn't make sense for rain falling from above. The rate of change of $\theta$ must approach zero so that $\theta$ does not pass 90$^\circ$.
A: It sounds to me like you understand it.
The change in $\theta$ isn't constant, because $\frac {d \theta}{dt}$ varies with $t$.
This just means that the umbrella wouldn't be rotating with a uniform angular velocity.  It varies with respect to how long they have been travelling.
It makes sense that it asymptotically stops changing angle, because at high speeds, the rain will be approximately horizontal relative to the moving person.  If change in angle over time was constant, this could not be the case, it would keep going below horizontal as time went on.
