The rate of change of the area of a circle with respect to its radius at $r = 3 \text{ cm}$ is . . . . . . $\text{cm}^2/\text{cm}$. (in $\pi$)

If the distance $s$ travelled by a particle in time $t$ is given by $s=t^2-2t+5$,then its acceleration is

The point on the curve $y^2 = 18x$,at which the rate of change of $Y$-coordinate is twice the rate of change of $X$-coordinate is . . . . . . . $\left(\frac{dx}{dt} \neq 0\right)$

The area of a square increases at the rate of $0.5 \text{ cm}^2/\text{sec}$. The rate at which its perimeter is increasing when the side of the square is $10 \text{ cm}$ long,is

The distance travelled $s$ (in $cm$) by a particle in $t$ seconds is given by $s = t^3 + 2t^2 + t$. The speed of the particle after $1$ second will be ......... $cm/sec$.

The edge of a cube is increasing at the rate of $5 \, cm/\sec$. How fast is the volume of the cube increasing when the edge is $12 \, cm$ long? (in $cm^3/\sec$)