An object starts a linear motion with velocity $'u^{\prime}$ and with uniform acceleration ' $a^{\prime}$, it acquires a velocity $'v^{\prime}$ in timet
$(a)$ Draw its velocity$-$time graph.
$(b)$ Obtain Ist equation of motion, $v=u+a t,$ for velocity $-$ time relation by using velocity$-$time graph.
$(c)$ A body moving with a velocity of $2\, m s ^{-1}$ acquires a velocity of $10 \,m s ^{-1}$ in $5\, s$. Find its acceleration.
$(a)$ The $v-t$ graph is as shown
$(b)$ Now, slope of the $v-t$ graph gives the acceleration of the motion.
$a=\frac{v-u}{t-0}=\frac{v-u}{t}$
Hence, $v=u+a t$
$(c)$ By using velocity - time graph
$u=2 m s ^{-1}, v=10 m s ^{-1}, t=5 s$
Using the expression $v=u+a t,$ we have
$a=\frac{10-2}{5-0}=\frac{8}{5}=1.6 m s ^{-2}$
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.
A piece of stone is thrown vertically upwards. It reaches its maximum height in $3$ second. If the acceleration of the stone be $9.8\, m s ^{-2}$ directed towards the ground, calculate the initial velocity of the stone with which it is thrown upwards. Find the maximum height attained by it.
The velocity$-$time graph of a truck is plotted below
$(a)$ Calculate the magnitude of displacement of the truck in $15$ seconds.
$(b)$ During which part of the journey was the truck decelerating ?
$(c)$ Calculate the magnitude of average velocity of the truck.
Draw displacement$-$time graphs for the following situations
$(i)$ When body is stationary.
$(ii)$ When body is moving with uniform velocity.
$(iii)$ When body is moving with variable velocity.
A body is thrown vertically upward with velocity $u$, the greatest height $h$ to which it will rise is,