Solving a Car Intersection Dilemma

[MrKoffee]

I believe at this point I am just confusing myself.

A car is approaching an intersection at a velocity of 20 m/s. When the car is 50 meters from the intersection the light turns yellow. The light will remain yellow for 3 seconds. The intersection is 20 meters in width. The driver can either hit the brakes for an acceleration of -3.8 m/s^2 or hit the gas to accelerate at 2.3 m/s^2. The car is 3.5m in length. (ignore driver reaction time). If the driver accelerates will he be able to clear the intersection, or should he brake. If he brakes can he come to a stop without entering the intersection.

So.

V0 is 20m/s
S0 is 0m
a is -3.8 or 2.3 m/s^2
t is 3 seconds.

I believe I should do the following

1/2(a)t^2+V0t+S0

giving

1/2(-3.8)(3^2)+20(3) = 42.9 meters to stop
or
1/2(2.3)(3^2)+20(3) = 70.35 meters when hitting the gas.

70.35m (distance driven) - 3.5 (length of the car) means that the tail end of the car is at 66.85m and did not clear the intersection.


have I reached the correct answer in the correct fashion or have I missed something?

Thanks for the help...

 

[Galileo]

Why is it important the car clears the intersection before the traffic light goes red? It's fine to drive through a yellow traffic light which the car easily makes by accelerating. Although a speed of 20+2.3(3) m/s = 96.8 km/h is considered speeding.

Anyhoo, everything looks ok.

 

[MrKoffee]

I personally don't care if the last 2 meters of the car is in the intersection when the light turns red, however, the problem in the textbook stated that it had to clear the intersection before it turned red.

Thanks for the review of the problem, I looked at it for while and started confusing myself with all the formulas...