Vroom, vroom! As soon as a traffic light turns green, a car
speeds up from rest to 50.0 mi/h with constant acceleration
9.00 mi/h + s. In the adjoining bike lane, a cyclist
speeds up from rest to 20.0 mi/h with constant acceleration
13.0 mi/h + s. Each vehicle maintains constant velocity
after reaching its cruising speed. (a) For what time
interval is the bicycle ahead of the car? (b) By what maximum
distance does the bicycle lead the car?
Doing part a.
The Attempt at a Solution
So my reasoning was that I need the position functions. I found them. I found the time at which the bike reaches its maximum velocity and selected that to be t=0. I adjusted both of the positions functions to this new setting.
Then I just went to solve for at what t they meet and my plan was just to add the (20/13) to that t and I would have the time at which the car overtakes the bike. However, I'm not successful in getting the right answer.
Where am I going wrong?
Picture of my homework posted below.