Answer
Displacement = $105m$.
Work Step by Step
we divide the interval into two sections: $[0,2]$ and $[2,5]$.
The velocity on each sub interval is approximated by evaluating v at the midpoint of that sub interval:
$v((2+0)/2) = v(1) = 15 m/s$ and $v((5+2)/2) = v(3.5) = 25 m/s$
we now know the height of our rectangles. To determine the area, we multiply by the width, or change in $t$.
$15 m/s * (2-0) s = 30m$ and $25 m/s * (5-2) s = 75m$
so, $30m + 75m = 105m$.
