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

If a spherical balloon has a variable diameter $d = 3x + \frac{9}{2}$ units, then the rate of change of its volume $V$ with respect to $x$ is:

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

$A$ particle is fired straight up from the ground. Its height in feet after $t$ seconds is given by $s(t) = 128t - 16t^2$. The velocity of the particle when it hits the ground is...

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 ...... $\text{cm/min}$.

$A$ ladder of length $13 \ m$ has one end resting against a vertical wall and the other on the ground. If the lower end moves away from the wall at a speed of $2 \ m/min$, then the speed (in $m/min$) at which the upper end falls when the bottom is $5 \ m$ away from the wall is