You are driving along a two lane high way at 50 mph. An approaching car traveling 50 mph the other way is a quarter mile ahead of you. You wish to pass a 40 ft long RV going 40 mph with its rear bumper 70 ft in front of your front bumper. Your car is 12 ft long. What constant acceleration would allow you to pass the RV and change back into your lane just as the bumpers of the RV and on-coming car are exactly your car's length apart, assuming the other vehicles remain at constant speed? What is the answer if you provide 70 ft of clearance between your car and each of the other two vehicles?
The Attempt at a Solution
I used the second equation to find the acceleration of my car. (50mph)^2 = 2a(122ft)
I used 122ft for the final position of my car because my car is 70ft away from the RV, the length of my car is 12ft, and the length of the RV is 40ft which is a total of 122ft. I solved for a which is acceleration and got $54347.83 mi/h^2$ which seemed a little big. I converted it to seconds and got 15.1 mi/s^2. Is this the correct way to approach this problem?
*edit could someone PM me how to use LaTex commands on this forum? Thanks!