The equation of motion of a car is $s = t^2 - 2t$,where $t$ is measured in hours and $s$ in kilometers. When the distance travelled by the car is $15 \, km$,the velocity of the car is ......... $km/h$.

The radius of a circle is increasing uniformly at the rate of $3 \, cm/s$. The rate of increase of its area when the radius is $10 \, cm$ will be:

Sand is pouring from a pipe at the rate of $12 \text{ cm}^3/\text{s}$. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is $4 \text{ cm}$?

$A$ body moves according to the formula $v = 1 + t^2$,where $v$ is the velocity at time $t$. The acceleration after $3 \text{ s}$ will be .......... $\text{cm/s}^2$. ($v$ is in $\text{cm/s}$)

Find the rate of change of $\sqrt{x^2 + 16}$ with respect to $\frac{x}{x - 1}$ at $x = 3$.

After $t$ seconds,the acceleration of a particle,which starts from rest and moves in a straight line is $(8-\frac{t}{5}) \text{ cm/s}^2$. The velocity of the particle at the instant when the acceleration is zero is: (in $\text{ cm/s}$)