General physics problem involving velocity, acceleration, braking of a car

[munchy35]

1.

You are driving toward a traffic signal when it turns yellow. Your speed is the legal speed limit of v0=55 km/h.: your best deceleration rate has the magnitude a = 5.18 m/s^2. Your best reaction time to begin braking is T = .75S. To avoid having the front of your car enter the intersection after the light turns red, should you brake to a stop or continue to move at 55 km/h if the distance to the intersection and the duration of the yellow light are a) 40 m and 2.8 s, and b) 32 m and 1.8s? Give an answer of brake, continue, either (if either strategy works) or neither (if neither strategy works and the yellow duration is inappropriate).

2.
x = x0 + v0 t + .5at^2

any derivatives needed...dx/dt? dv/dt?


3.

well the first thing i tried was converting the 55 km/h to the correct units of m/s. so 55 km/h = roughly about 15.277778 m/s.

then i drew some pictures and realized i need to use a formula involving v0, time, distance, and acceleration. I'm just confused on how to use T=.75 s. I'm getting a physics tutor soon, but since i don't have one yet...i need a lot of help. i just don't even know where to begin.

 

[PhaseShifter]

This is similar to another question I saw here yesterday.
It's a two-part problem since the car doesn't begin to decelerate until the driver reacts. That's where the 0.75s comes in.

total distance traveled = distance covered before reaction + distance covered during deceleration