Quantity that designates the speed and direction in which a body moves. It can be represented graphically by an arrow (pointing in the direction of the motion), the length of which is proportional to the magnitude, or speed. For an object in circular motion, the direction at any instant is tangential to the circle at that point, and so is perpendicular to the radius at that point. The instantaneous speed of a vehicle, such as an automobile, can be determined by a speedometer, or mathematically by differential calculus. The average speed is the ratio of the distance traveled in any given time interval divided by the time taken.
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Speed sufficient for a body to escape from a gravitational centre of attraction without accelerating further. It decreases with altitude and equals the square root of 2 (about 1.414) times the speed needed to maintain a circular orbit at the same altitude. At the surface of Earth, disregarding atmospheric resistance, escape velocity is about 6.96 mi/second (11.2 km/second). Escape velocity from the surface of the Moon is about one-third of this.
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The rate of change of velocity is referred to as acceleration.
The instant velocity vector of an object that has positions at time and at time , can be computed as the derivative of position:
The equation for an object's velocity can be obtained mathematically by evaluating the integral of the equation for its acceleration beginning from some initial period time to some point in time later .
The final velocity v of an object which starts with velocity u and then accelerates at constant acceleration a for a period of time is:
The average velocity of an object undergoing constant acceleration is , where u is the initial velocity and v is the final velocity. To find the displacement, x, of such an accelerating object during a time interval, , then:
When only the object's initial velocity is known, the expression,
can be used.
This can be expanded to give the position at any time t in the following way:
These basic equations for final velocity and displacement can be combined to form an equation that is independent of time, also known as Torricelli's equation:
The above equations are valid for both Newtonian mechanics and special relativity. Where Newtonian mechanics and special relativity differ is in how different observers would describe the same situation. In particular, in Newtonian mechanics, all observers agree on the value of t and the transformation rules for position create a situation in which all non-accelerating observers would describe the acceleration of an object with the same values. Neither is true for special relativity. In other words only relative velocity can be calculated.
The kinetic energy is a scalar quantity.
Escape velocity is the minimum velocity a body must have in order to escape from the gravitational field of the earth. To escape from the earth's gravitational field an object must have greater kinetic energy than its gravitational potential energy. The value of the escape velocity from Earth is approximately 11100 m/s
Relative velocity is a measurement of velocity between two objects as determined in a single coordinate system. Relative velocity is fundamental in both classical and modern physics, since many systems in physics deal with the relative motion of two or more particles. In Newtonian mechanics, the relative velocity is independent of the chosen inertial reference frame. This is not the case anymore with special relativity in which velocities depend on the choice of reference frame.
If an object A is moving with velocity vector v and an object B with velocity vector w , then the velocity of object A relative to object B is defined as the difference of the two velocity vectors:
The radial and angular velocities can be derived from the Cartesian velocity and displacement vectors by decomposing the velocity vector into radial and transverse components. The transverse velocity is the component of velocity along a circle centered at the origin.