The equation of motion of a particle is $s = at^2 + bt + c$. If the displacement after $1 \text{ s}$ is $20 \text{ m}$,velocity after $2 \text{ s}$ is $30 \text{ m/s}$,and the acceleration is $10 \text{ m/s}^2$,then:

If the edge of a cube increases at the rate of $60 \, cm/s$,at what rate is the volume increasing when the edge is $90 \, cm$ (in $cm^3/s$)?

$A$ particle moves along a curve $y = \frac{2x^3 - 1}{3}$. The points on the curve at which the $y$-coordinate is changing $18$ times as fast as the $x$-coordinate are

$A$ particle moves along the curve $y=x^2+2x$. Then, the point on the curve such that the $x$ and $y$ coordinates of the particle change with the same rate is

$A$ cube of ice melts without changing its shape at a uniform rate of $4 \, cm^3/min$. The rate of change of the surface area of the cube,in $cm^2/min$,when the volume of the cube is $125 \, cm^3$,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: