“acceleration”的概念、定义、翻译、参考文献-科学参考

acceleration

Physics

Symbol a. The rate of increase of speed or velocity. It is measured in m s⁻². For a body moving linearly with constant acceleration a from a speed u to a speed v,

$a = (v - u) / t = (v^{2} - u^{2}) / 2 s$

where t is the time taken and s the distance covered.

If the acceleration is not constant it is given by dv/dt=d²s/dt². If the motion is not linear the vector character of displacement, velocity, and acceleration must be considered. See also rotational motion.

Mathematics

Suppose that a particle is moving in a straight line, with a point O on the line taken as origin and one direction taken as positive. Let x be the displacement of the particle at time t. The acceleration of the particle is equal to $\ddot{x}$ or d²x/dt², the rate of change of the velocity with respect to t. If the velocity is positive (that is, if the particle is moving in the positive direction), the acceleration is positive when the particle is speeding up and negative when it is slowing down. However, if the velocity is negative, a positive acceleration means that the particle is slowing down and a negative acceleration means that it is speeding up.

In the preceding paragraph, a common convention has been followed, in which the unit vector i in the positive direction along the line has been suppressed. Acceleration is in fact a vector quantity, and in the 1-dimensional case above it is equal to $\ddot{x} i$ .

When the motion is in two or three dimensions, vectors are used explicitly. The acceleration a of a particle is a vector equal to the rate of change of the velocity v with respect to t. Thus a=dv/dt. If the particle has position vector r, then $a = d^{2} r / d t^{2} = \ddot{r}$ . When Cartesian coordinates are used, r = xi + yj + zk, and then $\ddot{r} = \ddot{x} i + \ddot{y} j + \ddot{z} k$ .

If a particle is travelling in a circle with constant speed, it still has an acceleration because of the changing direction of the velocity. This acceleration is towards the centre of the circle and has magnitude $\frac{v^{2}}{r}$ where v is the speed of the particle and r is the radius of the circle.

Acceleration has the dimensions LT⁻², and the SI unit of measurement is the metre per second per second, abbreviated to ms⁻².

Chemical Engineering

The rate of change of speed or velocity with respect to time. If the acceleration is constant then the final velocity, v, of a body that is initially moving with a velocity u after time t, is $v = u + a t$ . If the acceleration is not constant, then the acceleration can be found from:
$a = \frac{d v}{d t} = \frac{d^{2} s}{d t^{2}}$

(p. 3) where s is the distance moved by the body. In the case of motion in a circle, the acceleration is $v^{2} / r$ and directed to the centre of the circle of radius r.

Biology

A form of heterochrony in which, during the course of evolution, the rate of development of an organism is speeded up and new stages are added to the end of the ancestral developmental sequence without prolonging the total development time. The morphological outcome is an example of peramorphosis, and the developmental sequence (ontogeny) conforms to the theory of recapitulation.

Geology and Earth Sciences

1. An increase in speed or velocity.
2. Evolution that occurs by increasing the rate of ontogenetic (see ontogeny) development, so that further stages can be added before growth is completed. This form of heterochrony was proposed by E. H. Haeckel as one of the principal modes of evolution.

单词	acceleration
释义	acceleration Physics Symbol a. The rate of increase of speed or velocity. It is measured in m s⁻². For a body moving linearly with constant acceleration a from a speed u to a speed v, $a = (v - u) / t = (v^{2} - u^{2}) / 2 s$ where t is the time taken and s the distance covered. If the acceleration is not constant it is given by dv/dt=d²s/dt². If the motion is not linear the vector character of displacement, velocity, and acceleration must be considered. See also rotational motion. Mathematics Suppose that a particle is moving in a straight line, with a point O on the line taken as origin and one direction taken as positive. Let x be the displacement of the particle at time t. The acceleration of the particle is equal to $\ddot{x}$ or d²x/dt², the rate of change of the velocity with respect to t. If the velocity is positive (that is, if the particle is moving in the positive direction), the acceleration is positive when the particle is speeding up and negative when it is slowing down. However, if the velocity is negative, a positive acceleration means that the particle is slowing down and a negative acceleration means that it is speeding up. In the preceding paragraph, a common convention has been followed, in which the unit vector i in the positive direction along the line has been suppressed. Acceleration is in fact a vector quantity, and in the 1-dimensional case above it is equal to $\ddot{x} i$ . When the motion is in two or three dimensions, vectors are used explicitly. The acceleration a of a particle is a vector equal to the rate of change of the velocity v with respect to t. Thus a=dv/dt. If the particle has position vector r, then $a = d^{2} r / d t^{2} = \ddot{r}$ . When Cartesian coordinates are used, r = xi + yj + zk, and then $\ddot{r} = \ddot{x} i + \ddot{y} j + \ddot{z} k$ . If a particle is travelling in a circle with constant speed, it still has an acceleration because of the changing direction of the velocity. This acceleration is towards the centre of the circle and has magnitude $\frac{v^{2}}{r}$ where v is the speed of the particle and r is the radius of the circle. Acceleration has the dimensions LT⁻², and the SI unit of measurement is the metre per second per second, abbreviated to ms⁻². Chemical Engineering The rate of change of speed or velocity with respect to time. If the acceleration is constant then the final velocity, v, of a body that is initially moving with a velocity u after time t, is $v = u + a t$ . If the acceleration is not constant, then the acceleration can be found from: $a = \frac{d v}{d t} = \frac{d^{2} s}{d t^{2}}$ (p. 3) where s is the distance moved by the body. In the case of motion in a circle, the acceleration is $v^{2} / r$ and directed to the centre of the circle of radius r. Biology A form of heterochrony in which, during the course of evolution, the rate of development of an organism is speeded up and new stages are added to the end of the ancestral developmental sequence without prolonging the total development time. The morphological outcome is an example of peramorphosis, and the developmental sequence (ontogeny) conforms to the theory of recapitulation. Geology and Earth Sciences 1. An increase in speed or velocity. 2. Evolution that occurs by increasing the rate of ontogenetic (see ontogeny) development, so that further stages can be added before growth is completed. This form of heterochrony was proposed by E. H. Haeckel as one of the principal modes of evolution.
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