Rate measure practice · Mixed difficulty

If the volume of a spherical ball is increasing at the rate of $4 \pi \mathrm{cc} / \mathrm{sec}$, then the rate of increase of its radius (in cm/sec), when the volume is $288 \pi \mathrm{cc}$,

If the rate of increase of a side of a triangle inscribed in a circle of radius $\mathrm{R}$, is $\mathrm{R}$ times the rate of increase of the measure of opposite angle, then the measure of the angle is ....... .

For a particle moving in a straight line, if time $t$ be regarded as a function of velocity $v$, then the rate of change of the acceleration a is given by

The rate of change of the surface area of a sphere of a sphere of radiusr,when the radius is increasing at the rate of 2 cm/sis proportional to

The radius of a circular plate is increasing at the rate of 0.01 cm/s when the radius is 12 cm. Then , The rate at which the area increase, is

A point on the parabola ${y^2} = 18x$ at which the ordinate increases at twice the rate of the abscissa, is

A stone thrown upwards, has equation of motion $s = 490t - 49{t^2}.$ .Then, the maximum height reached by it ,is

If there is an error of $2\%$ in measuring the length of a simple pendulum, then percentage error in its period is

A rocket, weighing 9000 N fixed vertically upward. The gasses are expelled at a rate of $30\,\,{\text{kg}}\,{{\text{s}}^{ - 1}}$ with a speed of 0.6 km/s if the rocket weight 5000 N at the burnout, then the net upward force on the rocket at fire off should be

The displacement of a body along the X –axis depends on time as $\sqrt x = t + 2$ then the velocity of body

If a particle moves according to the law $s = 6{t^2} - \frac{{{t^3}}}{2}$, then the time at which it is momentarily at rest is

If the distance s covered by a particle in time t is proportional to the cube root of its velocity, then the acceleration is

If a particle is moving with velocity $v\left( t \right) = \cos \,\,\pi t$ along a straight line such that at $t = 0,\;\,s = 4$ its position function is given by

A particle moves on the parabola ${y^2} = 4ax$ in such a way that its projection on the $y$-axis has a constant velocity. Then its projection on $x$-axis moves with

If $y = \frac{{x + c}}{{1 + {x^2}}}$ where $c$ is a constant, then when $y$ is stationary, $xy$ is equal to

A point is moving on $y = 4 - 2{x^2}$. The $x$-coordinate of the point is decreasing at the rate of 5 unit per second. Then, the rate at which $y$-coordinate of the point is changing when the point is at (1,2)is

The distance travelled by a motor car in $t$ seconds after the brakes are applied is s feet, where $s=22 t-12 t^2$. The distance travelled by the car before it stops, is

If $T=2 \pi \sqrt{\frac{l}{g}}$, then relative errors in $T$ and $l$ are in the ratio

If the velocity $v$ of a particle moving along a straight line and its distance $s$ from a fixed point on the line are related by ${\upsilon ^2} = {a^2} + {s^2},$ then its acceleration equals

The radius and height of a cylinder are equal. If the radius of the sphere is equal to the height of the cylinder, then the ratio of the rates of increase of the volume of the sphere and the volume of the cylinder is