You're driving a truck at night going 60mph. Your headlights extend to 150 ft ahead of the truck. At the end of that 150 ft is a deer. You're reaction time is .35 second. If it takes 36.7 feet to go from 30 mph to 0mph would you hit the deer? And if so, what time?

I've gotten as far as solving the time it takes to go from 30 to 0. after that I don't know what to do.
Can anyone help?

If you are really a truck driver traveling in a big truck you either can hit the deer or not. It depends on if you want an avoidable accident or not on your driving record. In the real world the truck driver probably hits the deer as it is hard to oversteer a big truck and not lose it to a jack knife situation. As far as how much time, who cares as the deer is going to be at the side of the road dead shortly anyway.

It's a pickup truck and I don't know if I hit it or not. It depends on if I'm going to fast to stop in the length I'm given

Too fast*

The trick here is knowing that if it takes a certain distance to stop from 30MPH, it takes 4 times that long to stop from 60MPH. Reason is because at twice the velocity your kinetic energy is 4 times as much (since KE = 1/2 mv^2). Yet the force that your brakes apply to slow you down is constant regardless of speed, and the work done by your brakes is W = Fd. Set these equal, and you see that d (the distance to stop) goes as velocity squared. Can you take it from here?

We haven't done anything with kinetic energy, but I can take a look in my book and I'm sure I can get it! Thanks!