Fill in the blanks:
$(a)$ If the distance covered by a particle is zero,then its displacement is ....... .
$(b)$ For an object moving with uniform acceleration $a$,the change in velocity during a time interval $\Delta t$ is ......... .
$(c)$ The time rate of change of position of an object is called .......... .

In what different ways can the velocity of an object be changed?

What is reaction time? On what does the reaction time depend?

$A$ parachutist drops freely from an aeroplane for $10\,s$ before the parachute opens. Then he descends with a net retardation of $2.5\,m/s^2$. If he bails out of the plane at a height of $2495\,m$ and $g = 10\,m/s^2$,his velocity on reaching the ground will be .......$m/s$.

$A$ monkey climbs up a slippery pole for $3 \ s$ and subsequently slips for $3 \ s$. Its velocity at time $t$ is given by $v(t) = 2t(3 - t)$ for $0 < t < 3$ and $v(t) = -(t - 3)(6 - t)$ for $3 < t < 6$ in $m/s$. It repeats this cycle until it reaches the height of $20 \ m$.
$(a)$ At what time is its velocity maximum?
$(b)$ At what time is its average velocity maximum?
$(c)$ At what time is its acceleration maximum in magnitude?
$(d)$ How many cycles (counting fractions) are required to reach the top?

At time $t=0$, a particle leaves the origin and moves in the positive direction of the $X$-axis. If the velocity of the particle varies as $v(t)=v_0(1-t/t_0)$, where $|v_0|=10 \ m/s$ and $t_0=10 \ s$, then the distance covered by the particle during the first $20 \ s$ is: (in $m$)