The displacement $S$ of a moving particle at a time $t$ is given by $S=5+\frac{48}{t}+t^3$. Then its acceleration when the velocity is zero,is

$A$ horse runs along a circle with a speed of $20 \, km/hr$. $A$ lantern is at the centre of the circle. $A$ fence is along the tangent to the circle at the point at which the horse starts. The speed with which the shadow of the horse moves along the fence at the moment when it covers $1/8$ of the circle is (in $km/hr$):

The rate of change of the area of a sphere with respect to its radius, when the radius is $6 \text{ cm}$, is . . . . . . . (in $\pi$)

$A$ man of height $1.8 \ m$ is moving away from a lamp post at the rate of $1.2 \ m/sec$. If the height of the lamp post is $4.5 \ m$,then the rate at which the shadow of the man is lengthening is .......... $m/sec$.

Water is being filled at the rate of $1 \, cm^3/sec$ in a right circular conical vessel (vertex downwards) of height $35 \, cm$ and diameter $14 \, cm$. When the height of the water level is $10 \, cm$,the rate (in $cm^2/sec$) at which the wet conical surface area of the vessel increases is

$A$ ladder $5 \ m$ in length is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $2 \ m/sec$. How fast is the height on the wall decreasing when the foot of the ladder is $4 \ m$ away from the wall?