 # what is the meaning of relative velocity?

11 years ago

The velocity of a body with respect to a second body; that is, its velocity in a reference frame where the second body is fixed.

For example, if the velocities of particles A and B are $\mathbf{v}_A$ and $\mathbf{v}_B$ respectively in terms of a given coordinate system, then the relative velocity of A with respect to B (also called the velocity of A relative to B, $\mathbf{v}_{A/B}$, or $\mathbf{v}_{A \mathrm{\ rel\ } B}$) is $\mathbf{v}_{A \mathrm{\ rel\ } B} = \mathbf{v}_A - \mathbf{v}_B$.

Conversely, the velocity of B relative to A is $\mathbf{v}_{B \mathrm{\ rel\ } A} = \mathbf{v}_B - \mathbf{v}_A$.

The expression "the velocity of A relative to B" is shorthand for "the velocity of A in the coordinate system where B is always at rest".

11 years ago

Dear Abhishek Choudhary,

When two objects, say A and B are moving with different velocities, then the velocity of one object A with respect to another object B is called relative velocity of object A w.r.t. B.

Thus the relative velocity of one object w.r.t. another is the velocity with which one objects moves w.r.t. another object.

Mathematical definition of relative velocity is “time rate of change of relative position of one object with respect to another.”

i.e.

Relative velocity of object A w.r.t. object B,

VAB = velocity of object A- velocity of object B

= VAVB

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