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.

    52/550 (page 34)
    [63 (53). Let v0, v be the initial and final values of the speed of the moving point during the time t, a being the rate of change of speed. Then a = (v — v0)/t, and v = vQ + at. Hence the final speed is expressed in terms of the initial speed, the rate of change of speed, and the time. 64. As the speed increases uniformly with the time, its value at the middle of the interval is the arithmetic mean of its values at instants t seconds before, and t seconds after, the middle of the interval. Its value at the middle of the interval is therefore equal to the arithmetic mean of its initial and final values, and also to the mean speed during the interval. The mean speed is therefore equal to I K+K+at)]=vo+lat> Hence, if s denote the distance measured along the path between the initial and final positions of the moving point, s = (v0 + \at)t = v0t + hat2. Hence this distance also is expressed in terms of the initial speed, the rate of change of speed, and the time. 65. Eliminating t between these expressions for v and s (63 and 64) we find v- = v02 + 2as. Hence the final speed is expressed in terms of the initial speed, the rate of change of speed, and the length of path between the initial and final positions. 66. By means of the above equations, if the initial position of a point moving in a given path, its initial speed, and its uniform rate of change of speed be given, its final position and its final speed after any interval of time can be determined.