When will the average acceleration and instantaneous acceleration of a particle be equal over any time interval?

$A$ particle starts with an initial speed $u$ and retardation $a$ to come to rest in time $T$. The time taken to cover the first half of the total path travelled is .......

The velocity of a bullet is reduced from $200\,m/s$ to $100\,m/s$ while travelling through a wooden block of thickness $10\,cm$. Assuming the retardation to be uniform,the retardation will be:

$A$ particle moves along a straight line. Its position at any instant is given by $x = 32t - \frac{8t^3}{3}$,where $x$ is in $m$ and $t$ is in $s$. Find the acceleration of the particle at the instant when the particle is at rest $..........\,m/s^2$.

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement $(s)-$ velocity $(v)$ graph of this object is

$A$ particle moves a distance $x$ in time $t$ according to the equation $x = (t + 5)^{-1}$. The acceleration of the particle is proportional to: