. The Street railway journal . 26, and contained Figs. 1 to 10- thethird part, Aug. 9, and contained Figs. 11 to 13, and the fourth part, Aug 16and contained Fig. 14. dy o — = — = tan o° = v — zerodx dx that is to say, zero velocity, i. e., absolute rest. A curve such as shown in Fig. 15 is, in reality, a distance-timecurve, but is usually called simply a distance curve. From thepreceding analysis it will be readily seen that the slope of the curveor the angle which it makes with the axis of x, is an indication anda measure of the velocity of the moving body. It is also an in-dication of the d
. The Street railway journal . 26, and contained Figs. 1 to 10- thethird part, Aug. 9, and contained Figs. 11 to 13, and the fourth part, Aug 16and contained Fig. 14. dy o — = — = tan o° = v — zerodx dx that is to say, zero velocity, i. e., absolute rest. A curve such as shown in Fig. 15 is, in reality, a distance-timecurve, but is usually called simply a distance curve. From thepreceding analysis it will be readily seen that the slope of the curveor the angle which it makes with the axis of x, is an indication anda measure of the velocity of the moving body. It is also an in-dication of the direction of motion, for, as will be seen, the ele-mental motion (dy) taking place in the time (dx) is upward, sincethe space increment (dy) when measured on the scale of ordinatesrepresents the progression from the point y to the point y. In Fig. 1(1 we have a distance-time curve having a generaldownward slope. In this case, the elemental motion (dy) takingplace in the time (dx) is downward, since it represents the pro-. F1G. 15 gression irom the upper ordinate y to the lower ordinate y. Insuch a case the space increment (dy) would have a negative sign,and, dy consequently, the differential coefficient would have the dx negative sign. It follows, therefore, that in any distance-time curve, when thedifferential coefficient has a positive sign, it indicates motion up-ward, and when it has a negative sign, it indicates motion down-ward. The distance-time curve is related in an interesting manner tothe speed-time curve, which we now proceed to consider analyti-cally. In a speed-time curve (Figs. 1, 2, 3) the ordinate values (y)represent instantaneous values of speed or velocity, as previouslystated. We, therefore, have (from equation a) ds y = •— = v (b)dt It follows that the ordinates of a speed-time curve are porpor-tional to the differential coefficients, or the tangents, of a corres-ponding distance-time curve. Reciprocally, since integration isthe reverse of differe
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectstreetr, bookyear1884
