$A$ particle has an initial velocity of $10 \, m/s$. It moves due to a constant retarding force along the line of motion,which produces a retardation of $5 \, m/s^2$. Then:

The driver of a bus moving with a velocity of $72 \ km/h$ observes a boy walking across the road at a distance of $50 \ m$ in front of the bus and decelerates the bus at $5 \ m/s^2$ by applying brakes and is just able to avoid an accident. The reaction time of the driver is (in $s$)

The speed-time graph for a body moving along a straight line is shown in the figure. The average acceleration of the body may be .......... $m/s^2$.

$A$ 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?

$A$ particle moves along the sides $AB, BC, CD$ of a square of side $25 \, m$ with a constant velocity of $15 \, m \, s^{-1}$. Its average velocity is ........ $m \, s^{-1}$.

Two masses of $3.4 \text{ kg}$ and $2.5 \text{ kg}$ are accelerated from an initial speed of $5 \text{ m/s}$ and $12 \text{ m/s}$, respectively. The distances traversed by the masses in the $5^{th}$ second are $104 \text{ m}$ and $129 \text{ m}$, respectively. The ratio of their momenta after $10 \text{ s}$ is $\frac{x}{8}$. The value of $x$ is . . . . . . .