$A$ particle moves in a straight line so that its velocity at any point is given by ${v^2} = a + bx$,where $a, b \neq 0$ are constants. The acceleration is

Water is running into a hemispherical bowl of radius $180 \text{ cm}$ at the rate of $108 \text{ cubic decimetres per minute}$. How fast is the water level rising when the depth of the water level in the bowl is $120 \text{ cm}$? $(1 \text{ decimetre} = 10 \text{ cm})$

$A$ 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 $m/s$.

$A$ ladder makes an angle of $30^\circ$ with the wall. $A$ man is climbing the ladder at the rate of $3 \text{ ft/sec}$. What is the rate at which he is approaching the wall?

On dropping a stone in stationary water,circular ripples are observed. The rate of flow of ripples is $6 \text{ cm/sec}$. When the radius of the circle is $10 \text{ cm}$,the rate of increase in its area is:

If a particle moves such that the displacement $s$ is proportional to the square of the velocity $v$ acquired,then its acceleration is