How to calculate the stopping distance of a wheel collider?

How to calculate the stopping distance of a wheel collider?

I have an 'AI' bus in my game that needs to pull over occasionally at a bus stop. What I want to do is change the acceleration and brake force based on the stopping distance of the bus. I don't want to simply use the distance between the bus stop and the bus because each time the bus pulls over, it could be traveling at a different speed.
Right now it uses the distance between the bus stop and the bus. It doesn't really work well though because if a bus is traveling faster, it will take a longer distance to stop and will likely go past the bus stop. Same thing if it were going slower.
How do I calculate the stopping distance my bus will take to come to a complete stop?

Solutions/Answers:

Answer 1:

Let’s say that at some point in time you have the current speed v0 of your bus, which is at some position x0, and it needs to stop at position xs (s stands for stop).

TL;DR: You have to exert the following force f on the bus:

f = 0.5 * m * v0^2 / (x0 - xs)

where m is the mass of the bus.

Details:
The easiest way is to exert a constant force that will drive the bus to a parabolic (in time) curve ending exactly at the bus stop.
The equation for the position x at time t, and for the velocity v are

x = x0 + v0 * t + 0.5 * a * t^2
v = v0 + a* t

where a is the acceleration, which is what we want to calculate.
From the second equation, get t as a function of v, and plug into the first equation. In this way, you eliminate t and find the equation for x as function of v:

x = x0 + 0.5 * (v^2 - v0^2) / a

Now impose that at v = 0 you want x = xs, and solve for a. You get

a = 0.5 * v0^2 / (x0 - xs)

from which you get the force by multiplying with the mass m.

Answer 2:

I ended up using a simple speed-distance-time calculation, and a velocity calculation. This is the code I used:

float time = ((distance / currentSpeed) / timeFactor);

float acceleration = (-currentSpeed / time) / vFactor;

v = acceleration;

timeFactor and vFactor are just arbitrary values, which happened to be 1 and 15 respectively.

This may not work for most other people however as this was quite specific to my code.

References