EPT
For example, the first license exam requires you to accelerate from rest until the last possible moment and then slam on the brakes to come to a stop. The goal is to get the car parked a certain distance away in the minimum amount of time.
Problem with numbers: You need to get your car stopped exactly 400 meters away as quickly as possible. You accelerate from rest at a rate of 2 m/s^2 until you slam on the brakes, at which point your deceleration is 5 m/s^2. Find the amount of time after the race has started that you need to slam on your brakes in order to bring the car to a stop exactly 400 meters away.
Problem with letters: You need to get your car stopped exactly a distance D meters away as quickly as possible. You accelerate from rest at a rate of a m/s^2 until you slam on the brakes, at which point your deceleration is -b m/s^2. Find (in terms of letters):
A) an expression for the distance traveled by the car up until the moment the brakes were applied
B) an expression for the amount of time that elapses from when the brakes are first applied to when the car comes to a full stop
C) an expression for the total time elapsed during the trip
D) an expression for the distance traveled by the car from the moment the brakes were applied until the moment the car came to a stop
E) an expression for the top speed achieved by the car
F) an expression for total distance D in terms of t OR an expression for the time t in terms of D
G) an expression for the average speed of the car throughout the whole trip (why is there no b in this answer?)
I've worked this all out and will give anyone who wants to a chance to try this first. I'll probably do a banked road problem next as that's also pretty relevant to what I've been doing in gran turismo 5 =)
