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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....