A train which is traveling at 80 mi/hr applies its brakes as it reaches point A and slows down with a constant deceleration. Its decreased velocity is observed to be 60 mi/hr as it passes a point 1/2 mi beyond A. A car moving at 50 mi/hr passes point B at the same instant that the train reaches point A. In an unwise effort to beat the train to the crossing, the driver “steps on the gas.” Calculate the constant acceleration a that the car must have in order to beat the train to the crossing by 4 seconds and find the velocity v of the car as it reaches the crossing.

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Train A 1 mi 80 mi/hr Car Problem 2/24 50 mi/hr 1.3 mi