I want to compute the difference in time dependent on the maximum distance that is reached when a car overtakes another.
Assuming the use of two variables (time and horizontal distance) what function would be best in solving this problem. I imagine that the overtaking has a hemi-elliptical phase, we approach the car in front (horizontal distance = 0 than we start overtaking, horizontal distance increases to a maximum when cars are parallel to each other and than we return symmetrically until horizontal distance becomes 0).
If we neglect any physical phenomena, what function can be used to describe this pattern?
We have to assume that the movement of cars are uniform and continuous so the function can be derived (for example we can't imagine a trapezoid shape).
I think that this can be modeled with derivative of sin hyperbolic function. What do you think?