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

[mmoadi]

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?

 

[mgb_phys]

I think you made a typo on the caclulator
s = 13.8^2 / 2*3 = 31.7m

 

[mmoadi]

Thank you.