Car merging to main road: can it really be so simple?

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The discussion centers on calculating the minimum distance a car must be behind another vehicle on a main road to avoid catching up during merging. The merging car accelerates from rest at 3 m/s², while the other car travels at 50 km/h (13.89 m/s). Initial calculations suggested a distance of 4.38 m, which was questioned as being too small. A correction was proposed, leading to a recalculated distance of 31.7 m using the formula s = (v² - v0²) / 2a. The conversation highlights the importance of accurate calculations in determining safe merging distances.
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Homework Statement



Upon merging from side to main road and starting from rest with a constant acceleration 3 m/s². At the exact time of our merging, another car is driving on the main road in the same direction with speed 50 km/h. At least how far behind us should the car be, if we don’t want it to catch up with us?

Homework Equations



v^2 = v0^2 + 2as
s = (v^2 - v0^2) / 2a

The Attempt at a Solution



First I converted 50 km/h into 13.89 m/s.
For initial velocity I took 0, because the car starts from rest. For velocity I took the velocity of the second car, which is 50km/h (13.89m/s).

After plugging the numbers into the formula s = (v^2 - v0^2) / 2a, a got the result 4.38 m.
Somehow the distance seems too small?! Were my calculations correct?
 
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I think you made a typo on the caclulator
s = 13.8^2 / 2*3 = 31.7m
 
Thank you.
 

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