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In physics, Torricelli's equation, or Torricelli's formula, is an equation created by Evangelista Torricelli to find the final velocity of a moving object with constant acceleration along an axis (for example, the x axis) without having a known time interval. The equation itself is: [1] = + where
Instantaneous velocity of a falling object that has travelled distance on a planet with mass , with the combined radius of the planet and altitude of the falling object being , this equation is used for larger radii where is smaller than standard at the surface of Earth, but assumes a small distance of fall, so the change in is small and ...
According to a study a human at 70 kg (150 lb) requires about 60 watts to walk at 5 km/h (3.1 mph) on firm and flat ground, [6] while according to a calculator at kreuzotter.de the same person and power output on an ordinary bicycle will travel at 15 km/h (9.3 mph), [7] so in these conditions the energy expenditure of cycling is about one-third ...
Intuitively, the velocity increases linearly, so the average velocity multiplied by time is the distance traveled while increasing the velocity from v 0 to v, as can be illustrated graphically by plotting velocity against time as a straight line graph. Algebraically, it follows from solving [1] for
Oresme provided a geometrical verification for the generalized Merton rule, which we would express today as = (+) (i.e., distance traveled is equal to one half of the sum of the initial and final velocities, multiplied by the elapsed time ), by finding the area of a trapezoid. [3]
The braking a is from an initial speed u to a final speed v, over a length of time t. The equation u - v = at implies that the greater the acceleration the shorter the time needed to change speed. The stopping distance s is also shortest when acceleration a is at the highest possible value compatible with road conditions: the equation s = ut ...
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For example, in the case of spheres the angle depends on the distance between the (parallel) paths of the centers of the two bodies. Any non-zero change of direction is possible: if this distance is zero the velocities are reversed in the collision; if it is close to the sum of the radii of the spheres the two bodies are only slightly deflected.