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The discovery of the linear relationship between redshift and distance, coupled with a supposed linear relation between recessional velocity and redshift, yields a straightforward mathematical expression for Hubble's law as follows: = where v is the recessional velocity, typically expressed in km/s.
Since linear motion is a motion in a single dimension, the distance traveled by an object in particular direction is the same as displacement. [4] The SI unit of displacement is the metre . [ 5 ] [ 6 ] If x 1 {\displaystyle x_{1}} is the initial position of an object and x 2 {\displaystyle x_{2}} is the final position, then mathematically the ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
For a rotating object, the linear distance covered at the circumference of rotation is the product of the radius with the angle covered. That is: linear distance = radius × angular distance. And by definition, linear distance = linear speed × time = radius × angular speed × time. By the definition of torque: torque = radius × force.
The speed attained during free fall is proportional to the elapsed time, and the distance traveled is proportional to the square of the elapsed time. [41] Importantly, the acceleration is the same for all bodies, independently of their mass. This follows from combining Newton's second law of motion with his law of universal gravitation.
High-precision test of general relativity by the Cassini space probe (artist's impression): radio signals sent between the Earth and the probe (green wave) are delayed by the warping of space and time (blue lines) due to the Sun's mass. That is, the Sun's mass causes the regular grid coordinate system (in blue) to distort and have curvature.
Travelling a greater distance in the same time means a greater speed, and so linear speed is greater on the outer edge of a rotating object than it is closer to the axis. This speed along a circular path is known as tangential speed because the direction of motion is tangent to the circumference of the circle.
The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval; [2] the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero. Speed is the magnitude of velocity (a vector), which indicates additionally the direction of ...