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

The length $x$ of a rectangle is decreasing at the rate of $5 \text{ cm/min}$ and the width $y$ is increasing at the rate of $4 \text{ cm/min}$. When $x = 8 \text{ cm}$ and $y = 6 \text{ cm}$,find the rate of change of the perimeter.

An aeroplane at an altitude of $1 \text{ km}$ is flying horizontally at $600 \text{ km/hr}$, passes directly over an observer. The rate at which it is approaching the observer when it is $1250 \text{ meters}$ away from him is........ (in $\text{ km/hr}$)

If the surface area of a cube is increasing at a rate of $3.6 \text{ cm}^2/\text{sec}$,while maintaining its shape,then the rate of change of its volume (in $\text{cm}^3/\text{sec}$),when the length of a side of the cube is $10 \text{ cm}$,is:

$A$ man of height $2 \text{ m}$ walks at a uniform speed of $5 \text{ km/h}$ away from a lamp post which is $6 \text{ m}$ high. Find the rate at which the length of his shadow increases. (in $\text{ km/h}$)

$A$ point on the parabola $y^2 = \frac{36}{5}x$ at which the ordinate increases at thrice the rate of the abscissa is: