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

$A$ car moving along a straight line is brought to a stop within a distance of $200 \,m$ and in a time of $10 \,s$. The initial speed of the car is (in $\,ms^{-1}$)

$A$ particle moving along the $X$-axis has acceleration $f$ at time $t$ given by $f=f_0\left(1-\frac{t}{T}\right)$, where $f_0$ and $T$ are constants. The particle at $t=0$ has zero velocity. In the time interval between $t=0$ and the instant when $f=0$, the particle's velocity is

$A$ car passes three points $A$, $B$ and $C$ at $3 \text{ m/s}$, $6 \text{ m/s}$ and $9 \text{ m/s}$ respectively in a straight line with uniform acceleration. If distance $AB = 60 \text{ m}$, then find the distance $BC$. (in $m$)

Derive the equations of motion for constant acceleration using the method of calculus.

On what factors does the stopping distance depend?