The displacement $x$ of a particle at time $t$ is given by $x = At^2 + Bt + C$,where $A, B, C$ are constants and $v$ is the velocity of the particle. Then the value of $4Ax - v^2$ is:

The acceleration of a particle starting from rest and moving in a straight line with uniform acceleration is $8 \text{ m/s}^2$. The time taken by the particle to move the second metre is

After $t$ seconds,the acceleration of a particle,which starts from rest and moves in a straight line is $(8-\frac{t}{5}) \text{ cm/s}^2$. The velocity of the particle at the instant when the acceleration is zero is: (in $\text{ cm/s}$)

The equation of motion of a particle is given by $s = 2t^3 - 9t^2 + 12t + 1$,where $s$ and $t$ are measured in $cm$ and $sec$. The time when the particle stops momentarily is

$A$ balloon which always remains spherical is being inflated by pumping in $10 \text{ cm}^3$ of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is $15 \text{ cm}$.

$A$ point moves in a straight line during the time $t = 0$ to $t = 3$ according to the law $s = 15t - 2t^2$. The average velocity is