If the distance $s$ travelled by a particle in time $t$ is given by $s=t^2-2t+5$,then its acceleration is

The rate of change of the diagonal $R$ of a square with respect to its area $A$ is:

The speed $v$ of a particle moving along a straight line is given by $a + b{v^2} = {x^2}$ (where $x$ is its distance from the origin). The acceleration of the particle is

$A$ particle is fired straight up from the ground. Its height in feet after $t$ seconds is given by $s(t) = 128t - 16t^2$. The velocity of the particle when it hits the ground is...

The volume $V$ and depth $x$ of water in a vessel are connected by the relation $V = 5x - \frac{x^2}{6}$. If the volume of water is increasing at the rate of $5 \, cm^3/sec$,find the rate at which the depth of water is increasing when $x = 2 \, cm$.

$A$ particle is in motion along a curve $12 y = x^{3}$. The rate of change of its ordinate exceeds that of its abscissa when: