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

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:

$A$ stone is dropped into a quiet lake and waves move in circles at a speed of $8 \,cm/sec$. At the instant when the radius of the circular wave is $12 \,cm$, how fast is the enclosed area increasing?

$A$ container is in the shape of an inverted cone. Its height is $6 \ m$ and the radius at the top is $4 \ m$. If it is filled with water at the rate of $3 \ m^3/min$,then the rate of change of the height of the water (in $m/min$) when the water level is $3 \ m$,is

$A$ street light is at the top of a $12 \ m$ pole. $A$ man $2 \ m$ tall walks away from the pole towards a wall $12 \ m$ away from the pole at a speed of $1/2 \ m/s$. The rate at which his shadow on the wall is decreasing when he is $8 \ m$ from the wall is:

What will be the rate of change of the volume of a sphere with radius $r$,with respect to its diameter?