Answer
In 16 seconds, the runner runs a distance of $~~100~m$
Work Step by Step
To find the distance that the runner runs, we can find the area under the velocity versus time curve for the runner.
We can divide this area into four parts, including a triangle ($0~s$ to $2~s$), a rectangle ($2~s$ to $10~s$), a triangle ($10~s$ to $12~s$), and a rectangle ($10~s$ to $16~s$)
We can calculate each area separately:
$A_1 = \frac{1}{2}(2.0~s)(8.0~m/s) = 8.0~m$
$A_2 = (8.0~s)(8.0~m/s) = 64~m$
$A_3 = \frac{1}{2}(2.0~s)(4.0~m/s) = 4.0~m$
$A_4 = (6.0~s)(4.0~m/s) = 24~m$
We can find the total area:
$A = (8.0~m)+(64~m)+(4.0~m)+(24~m)$
$A = 100~m$
In 16 seconds, the runner runs a distance of $~~100~m$
