If the distance travelled by a point in time $t$ is $s = 180t - 16t^2$,then the rate of change in velocity is ......... $unit$.

If water is poured into a cylindrical tank of radius $3.5 \ ft$ at the rate of $1 \ ft^3/min$,then the rate at which the level of the water in the tank increases (in $ft/min$) is

$A$ 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

$A$ car starts from a point $P$ at time $t=0$ seconds and stops at point $Q$. The distance $x$,in metres,covered by it in $t$ seconds is given by $x=t^{2}(2-\frac{t}{3})$. Find the time taken by it to reach $Q$ and also find the distance between $P$ and $Q$.

$A$ point is moving on the curve $y=x^3-3x^2+2x-1$ and the $y$-coordinate of the point is increasing at the rate of $6 \text{ units/sec}$. When the point is at $(2, -1)$,the rate of change of the $x$-coordinate of the point is:

Let $x$ and $y$ be the sides of two squares such that $y = x - x^2$. The rate of change of the area of the second square with respect to the area of the first square is