$A$ particle moves along a straight line such that its distance $s$ in time $t$ seconds is given by $s = t + 6t^2 - t^3$. After what time is the acceleration zero?

If the volume of a spherical balloon is increasing at the rate of $900 \ cm^3/sec$,then find the rate of change of the radius of the balloon at the instant when the radius is $15 \ cm$ (in $cm/sec$).

If the rate of change of the area of a square $S$ is equal to its side length,and the rate of change of the side of $S$ is the same as that of a cube $C$,then the rate of change of the volume of $C$,at the time when its side length is $2$ units,will be ............ $units^3/sec$.

The total revenue received from the sale of $x$ units of a product is given by $R(x) = 10x^2 + 20x + 1500$. When $x = 1500$,the marginal revenue is . . . . . . .

Each edge of a cube is expanding at the rate of $1 \text{ cm/sec}$. Then the rate (in $\text{cc/sec}$) of change in its volume,when each of its edge is of length $5 \text{ cm}$,is

The length and breadth of a rectangle are $x \text{ cm}$ and $y \text{ cm}$ respectively. If the length decreases at the rate of $5 \text{ cm/min}$ and the breadth increases at the rate of $3 \text{ cm/min}$,then the rates of change of the perimeter and area respectively when $x = 5 \text{ cm}$ and $y = 2 \text{ cm}$ are: