Relative Velocity: Car A, B & C on Two Lane Road

In summary, the problem involves three cars - A, B, and C - traveling on a two-lane road. Car A is traveling at 36km/h while cars B and C are approaching it in opposite directions at 54km/h each. At a certain point when the distances between A and B and A and C are equal, car B decides to overtake A before C does. To avoid an accident, the minimum acceleration of B required is found by using the equation of motion for B, where the distance between A and B and A and C is 1km and the time it takes for C to overtake A is already known.
  • #1
arakram94
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on a two lane road, car A is traveling with a speed of 36km/h. two cars B and C approach car A in opposite direction with a speed of 54km/h each. at a certain instant, when distance AB is equal to AC both being 1km, B decides to overtake A before C does. what minimum acceleration of B is required to avoid accident?



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The Attempt at a Solution

 
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  • #2
Welcome to PF! :)
Consider a reference frame associated with the car A.
Solve this problem step by step:
What is the speed of B and C relative to the A?
How much time [tex]t_0[/tex] does it take for C to overtake A? (it's easy to calculate because C moves with a constant speed relative to the A)
Use the equation of motion for B:
[tex]x(t) = v_{0B} t + a t^2/2[/tex]
where [tex]v_{0B}[/tex] is a relative speed for B you've found earlier, [tex]a[/tex] -- unknown acceleration (it is the same in both laboratory (that is from your point of view) and moving relative to the A frames of references).
For a specific moment of time [tex]t=t_0[/tex], where [tex]t_0[/tex] you've already found this equation says:
[tex]L = v_{0B}t_0 + a t_0^2/2[/tex]
where L is the distance between A and B and A and C at the moment t=0, that is 1 km.
From this you'll find the acceleration.
 

Related to Relative Velocity: Car A, B & C on Two Lane Road

1. How is relative velocity calculated in the context of car A, B, and C on a two lane road?

Relative velocity is the measurement of the velocity of one object in relation to another. In the context of car A, B, and C on a two lane road, relative velocity can be calculated by subtracting the velocity of one car from the velocity of another car. For example, the relative velocity of car A with respect to car B would be the velocity of car A minus the velocity of car B.

2. How does the concept of relative velocity apply to two cars traveling in the same direction on a two lane road?

In the case of two cars traveling in the same direction on a two lane road, the relative velocity is equal to the difference in velocities of the two cars. If car A is traveling at 60 miles per hour and car B is traveling at 50 miles per hour, the relative velocity of car A with respect to car B would be 10 miles per hour.

3. What happens to the relative velocity if car C is traveling in the opposite direction as car A and B on a two lane road?

If car C is traveling in the opposite direction as car A and B, the relative velocity of car A with respect to car C would be the sum of their velocities. This is because the two cars are now moving towards each other, so their relative velocity would be the combination of their individual velocities.

4. Can relative velocity be negative?

Yes, relative velocity can be negative. This usually occurs when two objects are moving in opposite directions. In the context of car A, B, and C on a two lane road, if car A is traveling at a velocity of 60 miles per hour and car B is traveling at a velocity of 50 miles per hour in the opposite direction, the relative velocity of car A with respect to car B would be -10 miles per hour.

5. How does the distance between two cars on a two lane road affect their relative velocity?

The distance between two cars on a two lane road does not directly affect their relative velocity. The relative velocity is solely dependent on the velocities of the two cars. However, the distance between the two cars can affect their relative positions and the perception of their relative velocity. For example, if two cars are traveling at the same velocity but one is further ahead, it may appear to have a greater relative velocity to the other car.

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