I think I found the answers to the first two parts of this question but if you can check it and help me with the third part I would really appreciate it.
You are driving when a car passes you going 10 fps faster than you. You want to increase your speed to match his.
a)How long will it take, given that you can accelerate at a max of 2fps every second? My answer: 10/2=5 seconds to match speed.
b)If you begin you acceleration at exactly the moment he passes you, how far behind will you be when you match his speed? My answer: 10+8+6+4+2=30 Feet.
c)If you want to be exactly 45 feet behind him at the moment you match his speed, how long do you have to wait after he passes to begin acceleration. My answer: 1.5 seconds given that you will be 30 feet behind if you begin acceleration immediately so waiting 1.5 seconds means he will be an extra 15 feet ahead when you begin acceleration and 30+15 = 45 feet.
All help and input is appreciated!