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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    63] or a particle may be uniform or variable. Its value may- be the same at all instants of any interval of time, and therefore at all points of the path occupied during that time, or it may vary from point to point of the path and therefore from instant to instant. And, when the rate of change is variable, it may vary according to different laws. For example, it may vary directly as the distance of the moving point from a fixed point in its path (the distance being measured along the path), or inversely as this distance, or directly (or inversely) as the square of this distance, and so on. 61. Case I.—The Rate of Change of Speed being Zero. —In this case the speed is uniform. Hence the instan- taneous speed at any instant is equal to the mean speed during any interval (43), and therefore to the quotient of the length of path traversed in the time, by the time. If therefore v is the speed, and s the length of path traversed in t units of time, we have (42) v = s/t, and therefore s = vt. 62. Examples. (1) A point has a uniform speed of 10 ft. per see. Find the length of path traversed in 1 hour. Ans. 6-81 mis. (2) A point moves for 1 min. with uniform speed in a circle of 30 decimetres radius, traversing in that time an arc of 0-4 radian. Find the speed. Ans. 2 cm. per sec. (3) Find the time required by a point moving with a uniform speed of 40 cm. per sec. to traverse a path 20 metres long. Ans. 50 sec. 63. Case II.—The Rate of Change of Speed being Uniform.—In this case the instantaneous rate at any instant is equal to the mean rate during any interval c