Following are four different relations about displacement, velocity and acceleration for the motion of a particle in general. Choose the incorrect one (s).

Moderate

A

$\large {\text{v}}_{av} = \frac{1} {2}\left[ {{\text{v}}(t_1 ) + {\text{v}}(t_2 )} \right]$
B

${\text{v}}_{av} = \frac{{{\text{r}}(t_2 ) - {\text{r}}(t_1 )}} {{t_2 - t_1 }}$
C

${\text{r}} = \frac{1} {2}\left( {v(t_2 ) - v(t_1 )} \right)\left( {t_2 - t_1 } \right)$
D

${\text{a}}_{av} = \frac{{{\text{v}}(t_2 ) - {\text{v}}(t_1 )}} {{t_2 - t_1 }}$

Solution

${\text{Average velocity}} = \frac{{{\text{ Displacement}}}} {{{\text{Time interval}}}} = \frac{{r(t_2 ) - r(t_1 )}} {{(t_2 - t_1 )}}$
${\text{Average acceleration}} = \frac{{{\text{Change in velocity }}}} {{{\text{Time interval}}}} = \frac{{v(t_2 ) - v(t_1 )}} {{(t_2 - t_1 )}}$

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