1.) Your best friend Miguel, who controls the cartel's interests in South East Asia, is getting married in Karachi, Pakistan, and has invited you to the ceremony. Since you haven't seen Miguel in over a year you decide to suffer the 23 hour drive from Herat to Karachi. About halfway along your trip, just outside of Quetta, Pakistan, you notice that you are being followed. Both you and your pursuer begin to accelerate at constant rates. At one instant you are 4 km ahead, moving at 50 m/s, and accelerating at 0.5 m/s2. The other car is moving at 55 m/s and accelerating at 1.0 m/s2. How much time (in s) will elapse from this instant before you are caught?
2.) You are driving down K-10 late one night when a deer jumps out onto the road 100 m ahead of you. Because you were illegally texting while driving, you don't realize that the deer is in your path and step on the brakes until 1.5 s later. While skidding toward the deer your car is accelerating at a rate of -5 m/s2. What is the maximum initial speed (in m/s) you could have had to avoid hitting the deer?