# Kinematics : two cars meeting

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1. Nov 18, 2016

### PITPin

1. The problem statement, all variables and given/known data
Two cars leave at the same time (one from city A and the other from city B) and drive toward each other. They first meet d=45 km far from B . Both cars reach their destination (B for the former, A for the latter) and then start driving to their initial cities.The cars have constant acceleration. They meet a second time after t=3 hours from their first meeting. What is the speed of the vehicle which (initially) leaves from B?

2. Relevant equations
x=vt

3. The attempt at a solution
I tried fragmenting the problem. First I wrote the equations for the first meeting of the cars (d=vB*t0, D-d=vA*t0, where D is the distance between A and B) then the equations for the arrival of car B (the one which leaves from B) while car A has not yet arrived (I considered B to be faster). Then the equations for the arrival of car A and finally, the equations for the second meeting. I got 9 equations including the one for the time and I am not sure this is the right way to solve the problem. I also thought about considering the cars to be moving in a circle,but couldn't get enough equations.

I am sorry for any translation mistakes. I, myself, have found the original problem statement to be ambiguous, but I tried to translate it as accurate as possible.

2. Nov 18, 2016

### PeroK

If you have not already done so, can you derive the equation

$Dv_b = 45(v_a + v_b)$

where $D$ is the distance between the cities.

Last edited: Nov 18, 2016
3. Nov 18, 2016

### WrongMan

well.. 9 equations? thats alot...
what equations and unknowns did you get?
You need to conceptualize the problem, draw out the important moments ofthe problem and do the minimum equations and the minimum unknowns possible.
start by writing out the equations for the stated moments(first meet, reach city, second meet, reach city)
this has multiple possible answers!

4. Nov 18, 2016

### PeroK

There's only one answer for $v_b$.

5. Nov 18, 2016

### WrongMan

oh right my mistake

6. Nov 18, 2016

### PeroK

There are multiple solutions for $D$ and $v_a$, though.

7. Nov 18, 2016

### WrongMan

ah yes... not crazy after all... its just when i see these kind of problems i have to find all unknowns and forget i was only supposed to find one... and i dont allways write everything on paper...
now that i think (more) about it D cant change that much... carB has to get to A in at least 3 hours, right?

8. Nov 18, 2016

### PeroK

Yes, there must be upper and lower limits on $D$.

9. Nov 19, 2016

### PITPin

Can you please tell me more about this equation? I have just started using derivatives in physics and I'm having trouble understanding where this equation came from and what it means. Is D a function? If so, I think the result would be 45.

10. Nov 19, 2016

### PeroK

As I said, $D$ is just the distance between the cities. I was using your notation from post #1!