An elementary treatise on kinematics and dynamics / by James Gordon MacGregor.

  • MacGregor James Gordon, 1852-1913.
Date:
1902
Catalogue details

Licence: In copyright

Credit: An elementary treatise on kinematics and dynamics / by James Gordon MacGregor. Source: Wellcome Collection.

Provider: This material has been provided by the Royal College of Physicians of Edinburgh. The original may be consulted at the Royal College of Physicians of Edinburgh.

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    59] i.e., if the magnitudes of the units of rate of change of speed, of length, and of time, of one system of derived units be expressed in terms of the magnitudes of the corresponding units of another similarly derived system, the magnitude of the unit of rate of change of speed will be equal to the magnitude of the unit of length divided by the square of the magnitude of the unit of time. 59. Examples. (1) A point has at a given instant a speed of 4 ft. per sec.; and, after 8 sec, one of 20 ft. per sec. Find (a) the integral change of speed, and (6) the mean rate of change. Ans. (a) 16 ft. per sec.; (6) 2 ft.-per-sec. per sec. (2) If a point which moves in a curve traverse in t units of time after zero of tinie, an arc whose length s = 2t+'Stll + 4t3, find (a) the instantaneous speed, and (6) the instantaneous rate of change of speed, at the end of the 5th second. Ans. (a) 332 units of length per unit of time ; (6) 126 units of speed per unit of time. (3) If the foi'mula of Ex. 2 had been s = a/t + bt2 (a and b being constants), show that the instantaneous speed and rate of change of speed at the end of t units of time would have been 2bt — a/t2 and 2(a/t3 + b) respectively. (4) If the formula of Ex. 2 had been s = at + bt2, show that the rate of change of speed would have been uniform. (5) Find the number expressing the uniform rate of change of speed of a train which, 5 minutes after starting, is moving at the rate of 40 mis. per hour. Ans. 480 mls.-per-hour per hour. (6) Find how many kilometre-hour units of rate of change of speed are equivalent to 392 ft.-min. units. The magnitudes of the units involved in these systems are : [Z] = 1 kilometre ; [77] = 1 hour; [Z'] = l ft. =0-00030... kilom., [7] = 1 ni'n-='?S,» hour. Hence, if a be the equivalent required, we have,