$A$ particle moves in a straight line such that $s = \sqrt{t}$,then its acceleration is proportional to

The volume of a spherical ball is increasing at a rate of $4 \pi \text{ cm}^3 \text{ s}^{-1}$. The rate at which its radius increases,when its volume is $288 \pi \text{ cm}^3$,is ....... $\text{cm s}^{-1}$.

Two cyclists are moving from a junction of two roads inclined at an angle of $120^{\circ}$ to each other,with velocities of $4 \text{ km/h}$ and $3 \text{ km/h}$ respectively. The rate at which they are separating from each other after $1 \text{ hour}$ is ..... $\text{km/h}$.

$A$ bulb is placed at the centre of a circular track of radius $10 \ m$. $A$ vertical wall is erected touching the track at a point $P$. $A$ man is running along the track with a speed of $10 \ m/sec$. Starting from $P$, the speed with which his shadow is running along the wall when he is at an angular distance of $60^{\circ}$ from $P$ is: (in $m/sec$)

$A$ body moves according to the formula $v = 1 + t^2$,where $v$ is the velocity at time $t$. The acceleration after $3 \text{ s}$ will be .......... $\text{cm/s}^2$. ($v$ is in $\text{cm/s}$)

The radius of a circular plate is increasing at the rate of $0.01 \text{ cm/s}$ when the radius is $12 \text{ cm}$. Then,the rate at which the area increases,is