A train is traveling at a velocity of 77 feet per second when it hits its brakes. It slows down at a constant rate of 0.8 feet per second each second until it stops. DO NOT ROUND YOUR ANSWERS. 1) How long will it take the train to stop? Answer in decimal form. 2) After it hits its brakes, how many feet will it travel before it stops? Answer in decimal form.

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