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1) 96.25
2) 77 ft
We are given a velocity and a constant rate. With these two numbers, we can calculate how long it will take the train to stop and how many feet it will end up traveling before it stops.
We can take the velocity, subtract the constant rate times time (t), and set this equal to zero to find when the train will stop. We are using subtraction because the train is slowing down, so the constant rate is negative.
0 = 77 ft/sec - (0.8ft/sec * t)
-77 ft/sec = - (0.8ft/sec * t)
96.25 sec = t
It will take the train 96.25 seconds to stop once it starts breaking.
Next, we will find how many feet are traveled. We now know that it will take the train 96.25 seconds to stop, so we need to find the number of feet traveling during these 96.25 seconds.
We can use the distance formula to answer this question. Distance is equal to speed times time, and speed is the rate of change of distance. In other words, the speed will be |-0.8 ft/sec| = 0.8 ft/sec.
Distance = Speed * Time
Distance = 0.8 ft/sec * 96.25 sec
Distance = 77 ft