7.3 Relative acceleration

  Motion in One Dimension

    1.0 Introduction
    2.0 Kinematic variables
    3.0 Motion in one dimension
    4.0 Derivation of the kinematics equation
    5.0 Vertical motion under gravity
    6.0 Analysis of motion through graph
    7.0 Relative motion
    8.0 Simultaneous motion of two bodies
    9.0 River boat problem
    10.0 Aircraft-wind problem
    11.0 Rain problem

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7.3 Relative acceleration

When we differentiate relative velocity wrt time, we get relative acceleration.
$$\frac{{d{{\overrightarrow v }_{AB}}}}{{dt}} = \frac{{d{{\overrightarrow v }_A}}}{{dt}} - \frac{{d{{\overrightarrow v }_B}}}{{dt}}$$or$${\overrightarrow a _{AB}} = {\overrightarrow a _A} - {\overrightarrow a _B}$$ Similarly, $${\overrightarrow a _{BA}} = {\overrightarrow a _B} - {\overrightarrow a _A}$$
where,

${\overrightarrow a _A}:$ Acceleration of $A$ wrt origin (means the observer is at origin)
${\overrightarrow a _B}:$ Acceleration of $B$ wrt origin (means the observer is at origin)
${\overrightarrow a _{AB}}:$ Acceleration of $A$ wrt $B$ (means observer is $B$)

${\overrightarrow a _{BA}}:$ Acceleration of $B$ wrt $A$ (means observer is $A$)