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The velocity$-$time graph of an ascending passenger lift is as in the figure shown below
$(i)$ Identify the kind of motion of lift represented by lines $OA$ and $BC$.
$(ii)$ Calculate the acceleration of the lift
$(a)$ During the first two seconds.
$(b)$ Between the $3^ {r d}$ and $10^ {t h}$ second.
$(c)$ During the last two seconds.
Solution
$(i)$ Motion is represented by lines $OA$ and $BC$ which are uniformly accelerated and uniformly retarded motion.
$(ii)$ The acceleration of the lift
$(a)$ During the first two seconds (from $OA)$
$a=\frac{(v-u)}{t}=\frac{4.6-0}{2}=2.3 m s ^{-2}$
$(b)$ Between third and tenth second, the graph is a straight line parallel to the time axis. Hence, motion is uniform, acceleration $=0$
$(c)$ During the last two seconds (from $BC$)
$a=\frac{(v-u)}{t}=\frac{0-4.6}{12-10}=\frac{-4.6}{2}=-2.3 m s ^{-2}$
