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is the velocity of the Man relative to the Train, v T ∣ E {\displaystyle \mathbf {v} _{T\mid E}} is the velocity of the T rain relative to E arth. Fully legitimate expressions for "the velocity of A relative to B" include "the velocity of A with respect to B" and "the velocity of A in the coordinate system where B is always at rest".
In general for three objects A (e.g. Galileo on the shore), B (e.g. ship), C (e.g. falling body on ship) the velocity vector of C relative to A (velocity of falling object as Galileo sees it) is the sum of the velocity ′ of C relative to B (velocity of falling object relative to ship) plus the velocity v of B relative to A (ship's velocity ...
Then, the velocity of object A relative to object B is defined as the difference of the two velocity vectors: = Similarly, the relative velocity of object B moving with velocity w, relative to object A moving with velocity v is: = Usually, the inertial frame chosen is that in which the latter of the two mentioned objects is in rest.
Trajectory of a particle with initial position vector r 0 and velocity v 0, subject to constant acceleration a, all three quantities in any direction, and the position r(t) and velocity v(t) after time t. The initial position, initial velocity, and acceleration vectors need not be collinear, and the equations of motion take an almost identical ...
If point A has velocity components = (,,) and point B has velocity components = (,,) then the velocity of point A relative to point B is the difference between their components: / = = (,,) Alternatively, this same result could be obtained by computing the time derivative of the relative position vector r B/A .
Denote either entity by X. Then X moves with velocity u relative to F, or equivalently with velocity u′ relative to F′, in turn F′ moves with velocity v relative to F. The inverse transformations can be obtained in a similar way, or as with position coordinates exchange u and u′, and change v to −v.
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In the simplest case of two inertial frames the relative velocity between enters the transformation rule. For rotating reference frames or general non-inertial reference frames, more parameters are needed, including the relative velocity (magnitude and direction), the rotation axis and angle turned through.