snowboardalliance

Well, it's been a year since I took basic physics and I need some help. I'm working on a traffic simulation for a research job I have and I'm getting stuck trying to figure out the best way to do something.

Basically, I have two cars distance d apart each with a velocity and constant acceleration (well I'll call it constant for simplicity).

Now, if car number 1 is behind car number 2 and is traveling faster but has a negative acceleration, can it slow down before it hits car number 2?

So there is:

car1: s1 (position), v1, a1

car2: s2, v2, a2

d

conditions: s1 < s2, a1 < 0, and v1 > v2

I remember doing problems like this in physics, but I'm stuck.

EDIT:

I think I've figured it out,

the time to reach the same velocity is:

because

and if I just check that the distance of car1 at time t is less than the distance of car2 at time t + initial distance, then I know that the cars will not collide.

My problem is, if the accelerations are the same, it's division by 0 and I can't figure out an alternative equation or what that would really mean.

EDIT2:

Ok, I guess my calculation for time isn't really the time I want. What time would I need to plug in to:

To see if the car behind would hit the car in front?

Basically, I have two cars distance d apart each with a velocity and constant acceleration (well I'll call it constant for simplicity).

Now, if car number 1 is behind car number 2 and is traveling faster but has a negative acceleration, can it slow down before it hits car number 2?

So there is:

car1: s1 (position), v1, a1

car2: s2, v2, a2

d

conditions: s1 < s2, a1 < 0, and v1 > v2

I remember doing problems like this in physics, but I'm stuck.

EDIT:

I think I've figured it out,

the time to reach the same velocity is:

Code: |

v1 - v2 t = _______ a2 - a1 |

because

Code: |

vf = vi + at |

and if I just check that the distance of car1 at time t is less than the distance of car2 at time t + initial distance, then I know that the cars will not collide.

My problem is, if the accelerations are the same, it's division by 0 and I can't figure out an alternative equation or what that would really mean.

EDIT2:

Ok, I guess my calculation for time isn't really the time I want. What time would I need to plug in to:

Code: |

s = vi*t + 1/2at^2 |

To see if the car behind would hit the car in front?