Solving AP Mechanics Problem: Find DeltaTy for Vo & Minimal Time Interval

[fantolay]

Homework Statement

Assume you are driving at the speed limit V_o. As you approach an intersection 22m wide, you see the light turn yellow. During your reaction time of .6s, you travel at a constant speed as you recognize the warning, decide whether to stop or to go through the intersection, and move your foot to the brake if you must stop. Your car has good brakes and can accelerate at -2.4m/s². Before it turns red, the light should stay yellow long enough for you to be able to get to the other side of the intersection without speeding up, if you are too close to the intersection to stop before entering it. (Suggestion: You may find it easier to do part (a) after part (b).)

a) Find the required time interval DeltaT_y that the light should stay yellow in terms of V_o.
Evaluate answer for...
b) V_o = 8m/s
c) V_o = 11m/s
d) V_o = 18m/s
e) V_o = 25m/s

Evaluate your answer for...
f) V_o approaching zero
g) V_o approaching infinity
h) Describe pattern of variation of DeltaT_y with V_o. Account for answers to parts (f) and (g) physically.
i) For what value of V_o would Deltat_y be minimal?
j) What is the minimum time interval for part (i)?

Homework Equations

Probably the big 4 will be necessary in some form or another.

The Attempt at a Solution

I have no idea where to begin with this problem. I really don't even understand what it is asking and what is going on in the scenario.

I really appreciate any help.
Thanks guys.

 

[Delphi51]

Start with part (b) as suggested. Find the stopping distance and time. Find the time to coast through the intersection from the distance from which you could stop. The light must stay yellow for the minimum of these two times.