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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 ...
Equation [3] involves the average velocity v + v 0 / 2 . 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 ...
Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
The general formula for the escape velocity of an object at a distance r from the center of a planet with mass M is [12] = =, where G is the gravitational constant and g is the gravitational acceleration. The escape velocity from Earth's surface is about 11 200 m/s, and is irrespective of the direction of the object.
Instantaneous velocity can be defined as the limit of the average velocity as the time ... This differential equation ... physics is that forces can act at a distance ...
If is the length of the path (also known as the distance) travelled until time , the speed equals the time derivative of : [2] =. In the special case where the velocity is constant (that is, constant speed in a straight line), this can be simplified to v = s / t {\displaystyle v=s/t} .
Many other fundamental quantities in science are time derivatives of one another: force is the time derivative of momentum; power is the time derivative of energy; electric current is the time derivative of electric charge; and so on. A common occurrence in physics is the time derivative of a vector, such as velocity or displacement. In dealing ...
For a map distance of Δx AB, the first equation above predicts a midpoint Lorentz factor (up from its unit rest value) of γ mid = 1 + α(Δx AB /2)/c 2. Hence the round-trip time on traveler clocks will be Δτ = 4(c/α)cosh −1 [γ mid], during which the time elapsed on map clocks will be Δt = 4(c/α)sinh[cosh −1 [γ mid]].