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

[arakram94]

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?

Homework Equations

The Attempt at a Solution

 

[physicsworks]

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 $$t_0$$ 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:
$$x(t) = v_{0B} t + a t^2/2$$
where $$v_{0B}$$ is a relative speed for B you've found earlier, $$a$$ -- 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 $$t=t_0$$, where $$t_0$$ you've already found this equation says:
$$L = v_{0B}t_0 + a t_0^2/2$$
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.