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If two cars are moving in the same direction. let’s say ego car is in the front and another follower car. the speed, location in x, y coordinates of both cars are given.

How to calculates the distance between the cars in seconds? I have tried the following formula:

time = euclidean distance / (ego speed – follower speed), but something seems not correct.

Can anyone please answer?

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  • $\begingroup$ So what is it that seems incorrect? $\endgroup$
    – Anders Sandberg
    Commented Oct 22, 2019 at 22:23
  • $\begingroup$ I am getting really small values which kept me wondering since my simulation is showing huge distances. $\endgroup$
    – Sarah Jamal
    Commented Oct 22, 2019 at 22:27
  • $\begingroup$ You need to include a time variable in your formula .... the longer the cars have been travelling the greater the distance (and time) between the cars. $\endgroup$
    – PhysicsDave
    Commented Oct 22, 2019 at 23:09
  • $\begingroup$ Which time are you talking about? A time difference indicates a time period between two events - which two events? When the cars pass each other might be one event (they are at the same location), but what is the second event? Perhaps when they are a set distance apart? $\endgroup$
    – levitopher
    Commented Oct 23, 2019 at 3:15
  • $\begingroup$ @levitopher so basically I want to calculate the gap/distance between the cars in seconds. From the gap in time, I want to make a safety decision. $\endgroup$
    – Sarah Jamal
    Commented Oct 27, 2019 at 16:55

1 Answer 1

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Let $A$ be the first car and $B$ the second (follower). The relative speed between them is $v=v_A-v_B$. If the mean speed is constant, you can use the formula you described $$t=\frac{d}{v}$$ where d is the known distance at a time $t_0$. However, what does this equation tell you? If the cars have the same speed, time will be infinity, that is, $v=0$ and they will never meet. In cases $v_B<v_A$ or $v_B>v_A$ we are calculating the time $B$ will take to reach $A$ by assuming the latter stopped. It does not mean much more than this if you think about it.

Be sure you converted your units (km, seconds, etc...) to the correct ones.

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  • $\begingroup$ Thank you very much. you made the idea clear enough. $\endgroup$
    – Sarah Jamal
    Commented Oct 23, 2019 at 7:18

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