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1Rectilinear Motion with Constant Acceleration 1. On a certain stretch of track, trains run at 60 mph. How far back of a stopped train should a warning torpedo be placed to signal an oncoming train? Assume that the brakes are applied at once and retard the train at the uniform rate of 2 ft per sec2. 2. A stone is thrown vertically upward and returns to earth in l0sec. What was its initial velocity and how high did it go? 3. A ball is dropped from the top of a tower 80 ft high at the same instant that a second ball is thrown upward from the ground with an initial velocity of 40 ft per see. When and where do they pass, and with what relative velocity? 4. A stone is dropped down a well and 5 sec later the sound of the splash is heard. If the velocity of sound is 1120 ft per sec, what is the depth of the well? 5. A stone is dropped from a captive balloon at an elevation of 1000 ft. Two seconds later another stone is projected vertically upward from the ground with a velocity of 248 ft per sec. If g is 32 ft per sec2, when and where will the stones pass each other? 6. A stone is thrown vertically upward from the ground with a velocity of 48.3 ft per sec. One second later another stone is thrown vertically upward with a velocity of 96.6 ft per sec. How far above the ground will the stones be at the same level? 7. A ball is shot vertically into the air at a velocity of 193.2 ft per sec. After 4 sec, another ball is shot vertically into the air. What initial velocity must the second ball have in order to meet the first ball 386.4 ft from the ground? 8. A stone is thrown vertically up from the ground with a velocity of 300 ft per sec. How long must one wait before dropping a second stone from the top of a 600-ft tower if the two stones are to pass each other 200 ft from the top of the tower? 9. A ship being launched slides down the ways with a constant acceleration. She takes 8 sec to slide the first foot. How long will she take to slide down the ways if their length is 625 ft? 10. A train moving with constant acceleration travels 24 ft during the 10th sec of its motion and 18 ft during the 12th sec of its motion. Find its initial velocity and its constant acceleration. 11. An automobile starting from rest speeds up to 40 ft per sec with a constant acceleration of 4 ft per sec2, runs at this speed for a time, and finally comes to rest with a deceleration of 5 ft per sec2. If the total distance traveled is 1000 ft, find the total time required. 12. A train travels between two stations 1- mile apart in a minimum time of 41 sec. If the train accelerates and decelerates at 8 ft per sec2, starting from rest at the first station and coming to a stop at the second station, what is its maximum speed in mph? How long does it travel at this top speed? 13. Two cars A and B have a velocity of 60 mph in the same direction. A is 250 ft behind B when the brakes are applied to car B, causing it to decelerate at the constant rate of 10 ft per sec2.