The maximum height is reached in $5$ seconds by a stone thrown vertically upwards and moving under the equation $10s = 10ut - 49t^2$,where $s$ is in metres and $t$ is in seconds. The value of $u$ is ........ $m/sec$.

The $x$-coordinate changes on the curve $y=3x^5+15x-8$ at the rate of $\frac{1}{5} \text{ units/sec}$. If $A(x_1, y_1)$ and $B(x_2, y_2)$ are the points on the curve at which the $y$-coordinate changes at the rate of $6 \text{ units/sec}$, then the slope of $AB$ is:

The length $x$ of a rectangle is decreasing at the rate of $5 \text{ cm/min}$ and the width $y$ is increasing at the rate of $4 \text{ cm/min}$. When $x = 8 \text{ cm}$ and $y = 6 \text{ cm}$,find the rate of change of the perimeter.

If a particle moves in a straight line according to the law $x = a \sin (\sqrt{\lambda} t + b)$, then the particle will come to rest at two points whose distance is [symbols have their usual meaning]

$A$ ball thrown vertically upwards falls back on the ground after $6 \, s$. Assuming that the equation of motion is of the form $s = ut - 4.9t^2$,where $s$ is in metres and $t$ is in seconds,find the initial velocity $u$ at $t = 0$ in $m/s$.

$A$ balloon starting from rest is ascending from the ground with a uniform acceleration of $4 \ ft/sec^2$. At the end of $5 \ sec$, a stone is dropped from it. If $T$ is the time taken for the stone to reach the ground and $H$ is the height of the balloon when the stone reaches the ground, then: