POSSIBLE SOLUTION(S)

We'll first determine the top speeds on the Straight Path and the Curved Path.

We must determine the length of time that we will travel at top speed along the line. Since our maximum deceleration is 2 mph per second, we will have to spend a little more than 6 seconds slowing down from our top speed of 30 mph to our curve speed of about 17 mph.

Input := 

AccTime = ((MaxLineMPH - MaxTurnMPH) mph)/
				(2 mph/sec)

Output =

6.35698 sec

To determine how far we travel in that time, it will be helpful to get everything into feet per second rather than miles per hour.

Next we find the acceleration and deceleration distances (in feet).

The Straight Line distances (in feet) travelled at full speed are given by subtracting the distance from 1000 on each straight away on which the vehicle is either slowing down or speeding up. Then, the time to travel over these linear stretches is found by dividing by the speed.

Input := 

LineFt = 2 (1000 - AccFt)

Output =

1559.13

Input := 

LineTime = (LineFt ft)/(MaxLineFPS ft/sec)

Output =

35.4347 sec

The time (in seconds) spent on the turn.

Input := 

TurnFt = N[(Pi/2) 30]

Output =

47.1239

Input := 

TurnTime = (TurnFt ft)/(MaxTurnFPS ft/sec)

Output =

1.85872 sec

So the total time spent was

Input := 

LineTime + 2 AccTime + TurnTime

Output =

50.0073 sec