The position of an object moving along x-axis is given by x = a + $b{t}^2$, where a = 8.5 m and b = 2.5 m $s^{-2}$ and t is measured in seconds. The average velocity of the object between t = 2 s and t = 4 s is

Position is given as   $x=a+b{t}^2=8.5+2.5t^2$

Position at $t=2s$,  $x_2=8.5+2.5(2{)}^2=18.5m$

Position at $t=4s$,   $x_1=8.5+2.5(4{)}^2=48.5m$

Displacement  $S=x_2-x_1=48.5-18.5=30m$

Time taken  $t=4-2=2s$

Average velocity  $V_{avg}=\frac{S}{t}=\frac{30}{2}=15m/s$