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 ordinate of a point describing the circle $x^2 + y^2 = 25$ decreases at the rate of $1 \, cm/sec$. Find the rate of change of the abscissa of the point when the ordinate is equal to $3 \, cm$ (Given $x > 0, y > 0$).

Consider a rectangle whose length is increasing at the uniform rate of $2 \, m/sec$,breadth is decreasing at the uniform rate of $3 \, m/sec$ and the area is decreasing at the uniform rate of $5 \, m^2/sec$. If after some time the breadth of the rectangle is $2 \, m$,then the length of the rectangle is ........ $m$.

$A$ ladder $5 \ m$ in length is resting against a vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $1.5 \ m/sec$. The rate at which the height of the top of the ladder decreases when the foot of the ladder is $4.0 \ m$ away from the wall is .......... $m/sec$.

$A$ ladder of length $17 \,m$ rests with one end against a vertical wall and the other on the level ground. If the lower end slips away at the rate of $1 \,m/sec$, then when it is $8 \,m$ away from the wall, its upper end is coming down at the rate of

Water is being poured into a cylindrical vessel with a radius of $2 \text{ cm}$ at a rate of $8 \text{ cm}^3/\text{s}$. The rate at which the height of the water is increasing is: