The acceleration of a particle starting from rest and moving in a straight line with uniform acceleration is $8 \text{ m/s}^2$. The time taken by the particle to move the second metre is

The radius of a cylinder is increasing at a rate of $3 \text{ m/s}$ and its height is decreasing at a rate of $4 \text{ m/s}$. Find the rate of change of its volume when the radius is $4 \text{ m}$ and the height is $6 \text{ m}$.

$A$ balloon,which always remains spherical on inflation,is being inflated by pumping in $900 \, cm^3$ of gas per second. Find the rate at which the radius of the balloon increases when the radius is $15 \, cm$.

If the law of motion in a straight line is $s = \frac{1}{2}vt$,then acceleration is

If $pv = 81$,then $\frac{dp}{dv}$ at $v = 9$ is equal to

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 $\theta = \pi/4$.