The distance covered by a particle in $t$ seconds is given by $x = 3 + 8t - 4t^2$. After $1$ second, the velocity will be:

The surface area of a spherical ball is increasing at the rate of $4\pi \text{ cm}^2/\text{s}$. The rate at which the radius is increasing when the surface area is $16\pi \text{ cm}^2$ is (in $\text{ cm/s}$)

The rate of change of the volume of a sphere with respect to its surface area,when its radius is $2 \text{ cm}$,is

Gas is being pumped into a spherical balloon at the rate of $30 \, ft^3/min$. The rate at which the radius increases when it reaches the value $15 \, ft$ is:

$A$ point is in motion along a hyperbola $y = \frac{10}{x}$ such that its abscissa $x$ increases uniformly at a rate of $1 \text{ unit/s}$. Find the rate of change of its ordinate when the point passes through $(5, 2)$.

$A$ kind of bacteria grows by $t^3$ in $t \ s$. The time taken for the rate of growth of the bacteria to become $1200 \ \text{per } s$ is: (in $s$)