Relative Motion

Relative motion is the calculation of the movement of an object, relative to another observer or point of reference. Likewise, we can also find the relative velocity and acceleration between two points.

Position/velocity/acceleration of point $A$ relative to point $B$ is written as:
${\vec{r}}_{A/B},{\vec{v}}_{A/B},{\vec{a}}_{A/B}$

The $r/v/a$ of point $B$ relative to $A$ is equal and opposite to the $r/v/a$ of point $A$ relative to point $B$:
${\vec{r}}_{B/A}=-{\vec{r}}_{A/B}$

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Relative Position

• The absolute positions of two particles A and B with respect to the fixed $x,y,z$-reference frame are given by $r_A$ and $r_B$
• The position of B relative to A is represented by:
  $r_{B/A}=r_B-r_A$

Relative Velocity

The velocity of B relative to A is represented by:
${\vec{v}}_{B/A}={\vec{v}}_B-{\vec{v}}_A\text{OR}{\vec{v}}_B={\vec{v}}_A+{\vec{v}}_{B/A}$

Relative Acceleration

• The acceleration of B relative to A is represented by:
  $a_{B/A}=a_B-a_A\text{OR}{a}_B=a_A+a_{B/A}$

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