The sides of an equilateral triangle are increasing at the rate of $2 \ cm/s$. Find the rate at which its area is increasing when each side is $10 \ cm$.

The rate of change of the volume of a sphere with respect to its radius when $r = 7 \ cm$ is . . . . . . .

$A$ ladder $5 \ m$ in length is resting against a vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $1.5 \ m/sec$. The rate at which the height of the top of the ladder decreases when the foot of the ladder is $4.0 \ m$ away from the wall is .......... $m/sec$.

An ice layer of uniform thickness is deposited on an iron sphere of radius $10 \text{ cm}$. The ice melts at a rate of $50 \text{ cm}^3/\text{min}$. When the thickness of the ice layer is $5 \text{ cm}$,the rate at which the thickness of the ice layer is decreasing is ...... $\text{cm/min}$.

The volume of a spherical balloon is increasing at the rate of $40 \ cm^3/\min$. The rate of change of the surface area of the balloon at the instant when its radius is $8 \ cm$ is ........ $cm^2/\min$.

$A$ particle is moving on a straight line,where its position $s$ (in metre) is a function of time $t$ (in seconds) given by $s = at^2 + bt + 6, t \ge 0$. If it is known that the particle comes to rest after $4 \, s$ at a distance of $16 \, m$ from the starting position $(t = 0)$,then the retardation in its motion is