Constant Acceleration Kinematics: Car A is traveling at 22.0 m/s and car B at 29.0 m/s. Car A is 300 m behind car B when the driver of car A accelerates his car with a uniform forward acceleration of 2.40 m/s2. How long after car A begins to accelerate does it take car A to overtake car B?

The taken is  

Explanation:

Frm the question we are told that

  The speed of car A is  

   The speed of car B is  

     The distance of car B  from A is  

     The acceleration of car A is  

For A to overtake B

    The distance traveled by car B  =  The distance traveled by car A - 300m

Now the this distance traveled by car B before it is overtaken by A is  

Where is the time taken by car B

Now this can also be represented as using equation of motion as

Now substituting values

Equating the both d

substituting values

Solving this using quadratic formula we have that