When is the average velocity of an object equal to its instantaneous velocity?

The distance travelled by a particle is directly proportional to $t^{1/2}$,where $t =$ time elapsed. What is the nature of motion?

$A$ particle experiences a constant acceleration for $20 \,s$ after starting from rest. If it travels a distance ${S_1}$ in the first $10 \,s$ and a distance ${S_2}$ in the next $10 \,s$,then:

$A$ bullet enters a wooden block with velocity $120 \,m/s$. The bullet travels $1.5 \,s$ in the block before its velocity reduces to zero due to a resistance force which is proportional to the square root of the velocity. The distance travelled by the bullet in the wooden block is (in $\,m$)

The motion of a body is given by the equation $\frac{dv(t)}{dt} = 6.0 - 3v(t)$,where $v(t)$ is speed in $m/s$ and $t$ is in $s$. If the body was at rest at $t = 0$,which of the following statements is correct?

$A$ body moving with uniform acceleration travels a distance of $25 \ m$ in the fourth second and $37 \ m$ in the sixth second. The distance covered by the body in the next two seconds is: (in $m$)