# An Elementary Treatise on Analytic Mechanics with Numerous Examples

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1897 edition. Excerpt: ...the highest point of which shall be thgiven point and which shall touch the given line or curve. EXAMPLES 1. If the earth travels in its orbit 600 million miles in 365J days, with uniform motion, what is its velocity in miles per second? Ans. 19-01 miles. 2. A train of cars moving with a velocity of 20 miles an hour, had been gone 3 hours when a locomotive was dispatched in pursuit, with a velocity of 25 miles an hour; in what time did the latter overtake the former? Ans. 12 hours. 3. A body moving from rest with a uniform acceleration describes 90 ft. in the 5th second of its motion; find the acceleration, /, and velocity, v, after 10 seconds. Ans. f = 20; v = 200. 4. Find the velocity of a particle which, moving with an acceleration of 20 ft. per sec. has traversed 1000 ft. Ans. 200 ft. per sec. 5. A body is observed to move over 45 ft. and 55 ft. in two successive seconds; find the space it would describe in the 20th second. Ans. 195 ft. 6. The velocity of a body increases every hour at the rate of 360 yards per hour. What is the acceleration, /, in feet per second, and what is the space, s, described from rest in 20 seconds? Ans. / = 0.3; s = 00 ft. In these examples take g-39 ft. 7. A body is moving, at a given instant, at the rate of 8 ft. per sec.; at the end of 5 sees, its velocity is 19 ft. per sec. Assuming its acceleration to be uniform, what was its velocity at the end of 4 sees., and what will be its velocity at the end of 10 sees.? Ans. 16-8; 30. 8. A body is moving at a given instant with a velocity of 30 miles an hour, and comes to rest in 11 sees.; if the retardation is uniform what was its velocity 5 sees, before it stopped? Ans. 20 ft. per sec. 9. A body moves at the rate of 12 ft. a sec. with a uniform acceleration of 4;.