Kinematics : two cars meeting

In summary: I assume that ##v_a## and ##v_b## are the velocities of the two cars, and ##d## is the distance between them at the first meeting. Can you explain what you don't understand?In summary, the two cars start from different cities and drive towards each other, meeting at a distance of 45 km from one of the cities. They then continue to drive to their initial cities, with constant acceleration. After 3 hours from their first meeting, they meet again. The equation ##Dv_b = 45(v_a + v_b)## can be derived by considering the distances traveled by each car and setting them equal to each other. The value of ##D## is the distance between the cities, and ##
  • #1
PITPin
2
0

Homework Statement


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?

Homework Equations


x=vt

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.
 
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  • #2
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:
  • #3
well.. 9 equations? that's 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
WrongMan said:
well.. 9 equations? that's 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!
There's only one answer for ##v_b##.
 
  • #5
PeroK said:
There's only one answer for ##v_b##.
oh right my mistake
 
  • #6
WrongMan said:
oh right my mistake
There are multiple solutions for ##D## and ##v_a##, though.
 
  • #7
PeroK said:
There are multiple solutions for ##D## and ##v_a##, though.
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 don't allways write everything on paper...
now that i think (more) about it D can't change that much... carB has to get to A in at least 3 hours, right?
 
  • #8
Yes, there must be upper and lower limits on ##D##.
 
  • #9
PeroK said:
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.
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
PITPin said:
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.
As I said, ##D## is just the distance between the cities. I was using your notation from post #1!
 

1. How do you calculate the distance between two cars in a collision?

In order to calculate the distance between two cars in a collision, you will need to know the initial position, velocity, and acceleration of each car. From there, you can use the equations of kinematics to determine the distance traveled by each car and the point at which they meet.

2. What factors affect the speed at which two cars will meet?

The speed at which two cars will meet depends on a few factors, including their initial velocities, their acceleration, and the distance between them. The direction of each car's motion and the presence of external forces, like friction or air resistance, can also affect their meeting speed.

3. Can two cars meet at a constant speed?

Yes, two cars can meet at a constant speed if their initial velocities, acceleration, and direction of motion are all the same. In this case, they will continue to travel at the same speed until they meet, as long as there are no external forces acting on them.

4. How does the angle of collision affect the kinematics of two cars meeting?

The angle of collision can affect the kinematics of two cars meeting in a few ways. For example, if the cars are not traveling in the same direction, the angle of collision can change the direction of their trajectories. Additionally, the angle of collision can affect the forces acting on the cars, which can in turn affect their acceleration and overall motion.

5. What is the difference between elastic and inelastic collisions between two cars?

In an elastic collision, the total kinetic energy of the two cars is conserved, meaning that the cars will bounce off each other with no loss of energy. In an inelastic collision, some of the kinetic energy is converted into other forms of energy, like heat or sound, so the cars will not bounce off each other with the same speed. In both types of collisions, however, the total momentum of the two cars is conserved.

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