Calculating Time for Car B to Overtake Car A

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To determine how long it takes for Car B to overtake Car A, one must consider that Car A is 25 meters ahead and moving at a constant velocity, while Car B is accelerating. The calculation involves using kinematic equations for both cars, where the position of Car B must equal the position of Car A at the point of overtaking. By setting the difference in their positions to zero (P_B - P_A = 0), the time can be calculated based on Car B's acceleration and initial conditions. The approach is valid, as it accounts for Car B's initial velocity and acceleration. Thus, the method outlined is correct for finding the overtaking time.
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Say we have two cars, Car A and Car B. Car A is 25 meters ahead and has a constant velocity. Car B has the exact same velocity at the moment of observation, but also has a constant positive acceleration.

If I want to calculate how long it takes for Car B to overtake Car A, wouldn't it be the same as calculating how long it takes car B to go 25 meters from standing still?

I know how to calculate it if this is correct, I just need to know if it is.
 
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I think you can answer this one for yourself. Write the kinematic equations for both cars and and subtract them (if you want their positions equal, you want ##P_B - P_A = 0##. Set it equal to zero and see what happens.
 

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