7. Sami and Nitya are running a race. Sami is so confident in his ability to run, he gives Nitya a 12m head start and even lets her decide how long the race should be. The mastermind Nitya is, she knows Sami can start running almost instantly at 5m/s and maintains that speed, while she starts at rest and can accelerate at the rate of .5m/s' indefinitely. a. Find all possible distances Nitya should make the race so she wins. b. Find the time when Nitya and Sami have the same velocity