$A$ man $2 \text{ m}$ tall walks at the rate of $1 \frac{2}{3} \text{ m/s}$ towards a street light which is $5 \frac{1}{3} \text{ m}$ above the ground. The rate at which the length of his shadow is changing when he is $3 \frac{1}{3} \text{ m}$ away from the base of the light is . . . . . . (in $\text{ m/s}$)

$A$ point is in motion along a hyperbola $y = \frac{10}{x}$ such that its abscissa $x$ increases uniformly at a rate of $1 \text{ unit/s}$. Find the rate of change of its ordinate when the point passes through $(5, 2)$.

$A$ rod $AB$,$13 \text{ feet}$ long,moves with its ends $A$ and $B$ on two perpendicular lines $OX$ and $OY$ respectively. When $A$ is $5 \text{ feet}$ from $O$,it is moving away at the rate of $3 \text{ feet/sec}$. At this instant,$B$ is moving at the rate of:

If the displacement $S$ of a particle travelling along a straight line in $t$ seconds is given by $S = 2t^3 + 2t^2 - 2t - 3$,then the time taken (in seconds) by the particle to change its direction is

$A$ particle starts moving from rest from a fixed point in a fixed direction. The distance $s$ from the fixed point at a time $t$ is given by $s = t^{2} + at - b + 17$, where $a$ and $b$ are real numbers. If the particle comes to rest after $5 \ s$ at a distance of $s = 25$ units from the fixed point, then the values of $a$ and $b$ are respectively:

$A$ spherical balloon is expanding. If at any instant the rate of increase of its volume is $16$ times the rate of increase of its radius,then its radius at that instant is: