# Function to represent the acceleration of a car

I'm searching for a function that could represent the acceleration of a car. The function has to rise fast from $(0,0)$ to a maximum and then fall slower. For $x\to \infty$ it should go to $0$.

Regards

-
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. – Noah Snyder Nov 20 '12 at 13:20

from here: $a(t)= t\cdot e^{-k(t-t_0)}$
you can take any $\frac{f(t)}{g(t)}$ where $g(t),f(t)$ polynomials and $deg(g(t) \geq deg(f(t))$ just make sure $f(0)=0$ and $g(0)\ne0$. For example look at $\frac{t}{t^2 + 1}$