Two cyclists are moving from a junction of two roads inclined at an angle of $120^{\circ}$ to each other,with velocities of $4 \text{ km/h}$ and $3 \text{ km/h}$ respectively. The rate at which they are separating from each other after $1 \text{ hour}$ is ..... $\text{km/h}$.

$A$ ladder,$5 \ m$ long,rests against a vertical wall. If its top slides downwards at the rate of $10 \ cm/s$,then the angle between the ladder and the floor is decreasing at the rate of how many radians/second when its lower end is $4 \ m$ away from the wall?

Displacement $s$ of a particle at time $t$ is expressed as $s=2 t^3-9 t$. Find the acceleration at the time when the velocity vanishes.

$A$ swimming pool is to be drained for cleaning. If $L$ represents the number of litres of water in the pool $t$ seconds after the pool has been plugged off to drain and $L=200(10-t)^{2}$,how fast is the water running out at the end of $5$ seconds? What is the average rate at which the water flows out during the first $5$ seconds?

The distance $s$ in meters travelled by a particle in $t$ seconds is given by $s = \frac{2 t^3}{3} - 18 t + \frac{5}{3}$. The acceleration when the particle comes to rest is (in $m/s^2$)

$A$ spherical snowball is melting such that its volume is decreasing at the rate of $8 \text{ cm}^3/\text{s}$. Find the rate of change of the radius when the radius is $2 \text{ cm}$.