If a circular iron sheet of radius $30 \, cm$ is heated such that its area increases at the uniform rate of $6\pi \, cm^2/hr$,then the rate (in $cm/hr$) at which the radius of the circular sheet increases is

If a particle is moving in a straight line so that after $t$ seconds its distance $S$ (in $cm$) from a fixed point on the line is given by $S = f(t) = t^3 - 5t^2 + 8t$,then the acceleration of the particle at $t = 5 \text{ sec}$ is (in $cm/sec^2$).

The two equal sides of an isosceles triangle with a fixed base $b$ are decreasing at the rate of $3 \ cm/s$. How fast is the area decreasing when the two equal sides are equal to the base?

If the distance travelled by a point in time $t$ is $s = 180t - 16t^2$,then the rate of change in velocity is ......... $unit$.

$A$ particle moves along the curve $y=x^2+2x$. Then,the point on the curve such that the $x$ and $y$ coordinates of the particle change with the same rate is

If a metallic circular plate of radius $50 \, cm$ is heated so that its radius increases at the rate of $1 \, mm$ per hour,then the rate at which the area of the plate increases (in $cm^2/hour$) is (in $\pi$)