Can a particle moving in a straight line have zero velocity and non-zero acceleration at any instant? Give an example.

$A$ ball falls vertically downward and bounces off a horizontal floor. The speed of the ball just before reaching the floor $(u_1)$ is equal to the speed just after leaving contact with the floor $(u_2)$,where $u_1 = u_2$. The corresponding magnitudes of accelerations are denoted respectively by $a_1$ and $a_2$. The air resistance during motion is proportional to speed and is not negligible. If $g$ is the acceleration due to gravity,then:

$A$ ball is dropped from a high-rise platform at $t=0$ starting from rest. After $6$ seconds,another ball is thrown downwards from the same platform with a speed $v$. The two balls meet at $t=18\,s$. What is the value of $v$ in $m/s$? (Take $g= 10\,m/s^2$)

When a ruler falls vertically,$5$ different persons catch it with different reaction times. $(g = 9.8 \text{ ms}^{-2})$
$A$. Person $A$ has reaction time of $0.20 \text{ s}$
$B$. Person $B$ has reaction time of $0.22 \text{ s}$
$C$. Person $C$ has reaction time of $0.18 \text{ s}$
$D$. Person $D$ has reaction time of $0.19 \text{ s}$
$E$. Person $E$ has reaction time of $0.21 \text{ s}$
What is the correct order of the distance travelled by the ruler for each person?

$A$ stone is thrown vertically upwards with a velocity $V_0$ from a tower of height $h$ and it reaches the ground in time $t_1$. If the stone is thrown downwards with the same velocity $V_0$ from the same tower,it reaches the ground in time $t_2$. If the stone is dropped from the tower,it reaches the ground in time $t$. Find the value of $t$.

$A$ body is dropped from a height $H$. The time taken to cover the second half of the journey is: