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In
physics,
velocity is defined as the Derivative of position. It is a vector (spatial) physical quantity, both speed
and direction are required to define it. In the
SI (metric) system, it is measured in meters per second (m/s). The
scalar (physics) absolute value (
Magnitude (mathematics)) of velocity is
speed. For example, "5 metres per second" is a speed and not a vector, whereas "5 metres per second east" is a vector. The average velocity (
v) of an object moving through a displacement ( \Delta x) in a straight line during a time interval ( \Delta t) is described by the formula:
v = \frac{\Delta x}{\Delta t}.
Acceleration equals the change of velocity, or delta velocity, over a certain time interval.Solve for velocity which would be placed as X in the equation and simply solve for x and you have your velocity
Equations of motion
The instantaneous velocity vector (
v) of an object that has position
x(
t), at time
t, can be computed as the derivative:
v={\mathrm{d}x \over \mathrm{d}t} = \lim_{\Delta t \to 0}{\Delta x \over \Delta t}.
The equation for an object's velocity can be obtained mathematically by taking the
integral of the equation for its acceleration beginning from some initial period time
t_0 to some point in time later
t_n.
The final velocity
v of an object which starts with velocity
u and then accelerates at constant acceleration
a for a period of time ( \Delta t) is:
v = u + a \Delta t\!
The average velocity of an object undergoing constant
Acceleration is \begin{matrix} \frac {(u + v)}{2} \; \end{matrix}, where
u is the initial velocity and
V is the final velocity. To find the displacement,
s, of such an accelerating object during a time interval, \Delta t, then:
\Delta x = \frac {( u + v )}{2}\Delta t.
When only the object's initial velocity is known, the expression,
\Delta x = u \Delta t + \frac{1}{2}a \Delta t^2,
can be used.
This can be expanded to give the position at any time t in the following way:
x(t) = x(0) + \Delta x = x(0) + u \Delta t + \frac{1}{2}a \Delta t^2,
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:
v^2 = u^2 + 2a\Delta x.\,
The above equations are valid for both classical mechanics and
special relativity. Where classical mechanics and special relativity differ is in how different observers would describe the same situation. In particular, in classical 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 (
energy of motion), E_{K}, of a moving object is linear with both its
mass and the square of its velocity:
E_{K} = \begin{matrix} \frac{1}{2} \end{matrix} mv^2.
The kinetic energy is a
scalar (physics) quantity.
==Polar coordinates==In
Polar_coordinate_system, a two-dimensional velocity can be decomposed into a radial velocity, defined as the component of velocity away from or toward the origin (also known as
velocity made good), and
transverse velocity, the component of velocity along a circle centered at the origin, and equal to the distance to the origin times the angular velocity.
Angular momentum in scalar form is the distance to the origin times the transverse speed, or equivalently, the distance squared times the angular speed, with positive quantities representing counter-clockwise direction and negative quantities representing clockwise direction (in a right-handed coordinate system).
Velocity = \frac{Displacement}{Time}
If forces are in the radial direction only with an inverse square dependence, as in the case of a gravitational orbit, angular momentum is constant, and transverse speed is inversely proportional to the distance, angular speed is inversely proportional to the distance squared, and the rate at which area is swept out is constant. These relations are known as Kepler's laws of planetary motion
See also
References
- Halliday, David, Robert Resnick and Jearl Walker, Fundamentals of Physics, Wiley; 7 Sub edition (June 16, 2004). ISBN 0471232319.
External links
- Speed and Velocity (The Physics Classroom)
- Introduction to Mechanisms (Carnegie Mellon University)
In physics,
velocity is defined as the Derivative of position. It is a
vector (spatial) physical quantity, both speed
and direction are required to define it. In the SI (metric) system, it is measured in
meters per second (m/s). The
scalar (physics) absolute value (Magnitude (mathematics)) of velocity is
speed. For example, "5 metres per second" is a speed and not a vector, whereas "5 metres per second east" is a vector. The average velocity (
v) of an object moving through a displacement ( \Delta x) in a straight line during a time interval ( \Delta t) is described by the formula:
v = \frac{\Delta x}{\Delta t}.
Acceleration equals the change of velocity, or delta velocity, over a certain time interval.Solve for velocity which would be placed as X in the equation and simply solve for x and you have your velocity
Equations of motion
The instantaneous velocity vector (
v) of an object that has position
x(
t), at time
t, can be computed as the derivative:
v={\mathrm{d}x \over \mathrm{d}t} = \lim_{\Delta t \to 0}{\Delta x \over \Delta t}.
The equation for an object's velocity can be obtained mathematically by taking the integral of the equation for its acceleration beginning from some initial period time
t_0 to some point in time later
t_n.
The final velocity
v of an object which starts with velocity
u and then accelerates at constant acceleration
a for a period of time ( \Delta t) is:
v = u + a \Delta t\!
The average velocity of an object undergoing constant
Acceleration is \begin{matrix} \frac {(u + v)}{2} \; \end{matrix}, where
u is the initial velocity and
V is the final velocity. To find the displacement,
s, of such an accelerating object during a time interval, \Delta t, then:
\Delta x = \frac {( u + v )}{2}\Delta t.
When only the object's initial velocity is known, the expression,
\Delta x = u \Delta t + \frac{1}{2}a \Delta t^2,
can be used.
This can be expanded to give the position at any time t in the following way:
x(t) = x(0) + \Delta x = x(0) + u \Delta t + \frac{1}{2}a \Delta t^2,
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:
v^2 = u^2 + 2a\Delta x.\,
The above equations are valid for both
classical mechanics and
special relativity. Where classical mechanics and special relativity differ is in how different observers would describe the same situation. In particular, in classical 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 (
energy of motion), E_{K}, of a moving object is linear with both its
mass and the square of its velocity:
E_{K} = \begin{matrix} \frac{1}{2} \end{matrix} mv^2.
The kinetic energy is a
scalar (physics) quantity.
==Polar coordinates==In
Polar_coordinate_system, a two-dimensional velocity can be decomposed into a radial velocity, defined as the component of velocity away from or toward the origin (also known as
velocity made good), and
transverse velocity, the component of velocity along a circle centered at the origin, and equal to the distance to the origin times the angular velocity.
Angular momentum in scalar form is the distance to the origin times the transverse speed, or equivalently, the distance squared times the angular speed, with positive quantities representing counter-clockwise direction and negative quantities representing clockwise direction (in a right-handed coordinate system).
Velocity = \frac{Displacement}{Time}
If forces are in the radial direction only with an inverse square dependence, as in the case of a gravitational orbit, angular momentum is constant, and transverse speed is inversely proportional to the distance, angular speed is inversely proportional to the distance squared, and the rate at which area is swept out is constant. These relations are known as
Kepler's laws of planetary motion
See also
- Terminal velocity
- Hypervelocity
- Four-velocity (relativistic version of velocity for Minkowski spacetime)
- Rapidity (a version of velocity additive at relativistic speeds)
- Derivatives of displacement
References
- Halliday, David, Robert Resnick and Jearl Walker, Fundamentals of Physics, Wiley; 7 Sub edition (June 16, 2004). ISBN 0471232319.
External links
- Speed and Velocity (The Physics Classroom)
- Introduction to Mechanisms (Carnegie Mellon University)
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