If a particle moves such that the displacement $s$ is proportional to the square of the velocity $v$, then its acceleration $a$ is

The rate of change of the area of a sphere with respect to its radius, when the radius is $6 \text{ cm}$, is . . . . . . . (in $\pi$)

The displacement of a particle in time $t$ is given by $s = 2t^2 - 3t + 1$. The acceleration is

$A$ stone thrown vertically upwards has its motion described by the equation $s = 13.8t - 4.9t^2$,where $s$ is in meters and $t$ is in seconds. The velocity at $t = 1$ second will be ...... $m/s$.

Let $x$ be the length of one of the equal sides of an isosceles triangle,and let $\theta$ be the angle between them. If $x$ is increasing at the rate of $1/12 \ m/hr$,and $\theta$ is increasing at the rate of $\pi/180 \ \text{radians/hr}$,then find the rate in $m^2/hr$ at which the area of the triangle is increasing when $x = 12 \ m$ and $\theta = \pi/4$.

The volume of a spherical balloon is increasing at the rate of $40 \ cm^3/\min$. The rate of change of the surface area of the balloon at the instant when its radius is $8 \ cm$ is ........ $cm^2/\min$.