When are the acceleration and average acceleration equal for a moving object?

Two cars $A$ and $B$ initially at rest are moving in the same direction with accelerations $a_1$ and $a_2$ respectively. After a certain time $t$, they achieve velocities $v_1$ and $v_2$ respectively and are separated by a distance of $50 \ m$. If $(a_1 - a_2) = 4 \ m \ s^{-2}$, then the quantity $(v_1 - v_2)$ will be: (in $m \ s^{-1}$)

Tripling the speed of the motor car multiplies the distance needed for stopping it by

$A$ body is moving with a uniform acceleration covers $40\,m$ in the first $4\,s$ and $120\,m$ in next $4\,s.$ Its initial velocity and acceleration are

$A$ particle initially at rest starts moving from reference point $x=0$ along the $x$-axis,with velocity $v$ that varies as $v=4 \sqrt{x} \ m/s$. The acceleration of the particle is . . . . . . $m/s^2$.

$A$ particle moving with uniform acceleration travels $24\, m$ and $64\, m$ in the first two consecutive intervals of $4\, s$ each. Its initial velocity is ....... $m/s$.