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Velocity and acceleration in non-uniform circular motion. In non-uniform circular motion, an object moves in a circular path with varying speed. Since the speed is changing, there is tangential acceleration in addition to normal acceleration. The net acceleration is directed towards the interior of the circle (but does not pass through its center).
The linear motion can be of two types: uniform linear motion, with constant velocity (zero acceleration); and non-uniform linear motion, with variable velocity (non-zero acceleration). The motion of a particle (a point-like object) along a line can be described by its position x {\displaystyle x} , which varies with t {\displaystyle t} (time).
The net force on the object is zero, and the result is that the velocity of the object remains constant. Terminal velocity is the maximum speed attainable by an object as it falls through a fluid ( air is the most common example).
The SI unit for acceleration is metre per second squared (m⋅s −2, ). For example, when a vehicle starts from a standstill (zero velocity, in an inertial frame of reference) and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the vehicle turns, an acceleration occurs toward the new direction ...
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 ...
When considering atmospheric or oceanic dynamics, the vertical velocity is small, and the vertical component of the Coriolis acceleration () is small compared with the acceleration due to gravity (g, approximately 9.81 m/s 2 (32.2 ft/s 2) near Earth's surface). For such cases, only the horizontal (east and north) components matter.
All frames of reference with zero acceleration are in a state of constant rectilinear motion (straight-line motion) with respect to one another. In such a frame, an object with zero net force acting on it, is perceived to move with a constant velocity, or, equivalently, Newton's first law of motion holds. Such frames are known as inertial.
Velocity is then interpreted as rapidity, the hyperbolic angle for which the hyperbolic tangent function =. Acceleration, the change of velocity over time, then changes rapidity according to Lorentz transformations. This part of mechanics is special relativity.