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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 = = =.
In SI, this slope or derivative is expressed in the units of meters per second per second (/, usually termed "meters per second-squared"). Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the ...
The speed is 1 metre per second. The inward acceleration is 1 metre per square second, v 2 /r. It is subject to a centripetal force of 1 kilogram metre per square second, which is 1 newton. The momentum of the body is 1 kg·m·s −1. The moment of inertia is 1 kg·m 2. The angular momentum is 1 kg·m 2 ·s −1. The kinetic energy is 0.5 joule.
Consequently, the acceleration is the second derivative of position, [7] often written . Position, when thought of as a displacement from an origin point, is a vector: a quantity with both magnitude and direction. [9]: 1 Velocity and acceleration are vector quantities as well. The mathematical tools of vector algebra provide the means to ...
2007-05-21 18:57 Feeb denroc 512×512× (39102 bytes) Vector diagram showing the directions of velocity and acceleration on a particle as it moves in a uniform circular motion. Text has been converted to paths to render properly. Please see [[Circular motion velocity and acceleration.svg]] for editable text
Acceleration has the dimensions of velocity (L/T) divided by time, i.e. L T −2. The SI unit of acceleration is the metre per second squared (m s −2); or "metre per second per second", as the velocity in metres per second changes by the acceleration value, every second.
The first "centrifugal acceleration" term depends only on the radial position r and not the velocity of our object, the second "Coriolis acceleration" term depends only on the object's velocity in the rotating frame v rot but not its position, and the third "Euler acceleration" term depends only on position and the rate of change of the frame's ...
2007-05-21 17:35 Feeb denroc 512×512× (15216 bytes) Vector diagram showing the directions of velocity and acceleration on a particle as it moves in a uniform circular motion. Captions English
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