Question

Considering the stoplight example in the reading with velocity $v\left(t\right)=-0.22t^2+8.8t$as shown next at the left, approximate the distance travelled by dividing the time interval $[0,40]$into eight pieces and assuming constant velocity on each piece. Interpret this distance in terms of rectangles on the graph of $v\left(t\right)$.

Short answer

The distance is$2310feet.$

Step-by-step solution

Step 1. Given information.

The given function is$v\left(t\right)=-0.22t^2+8.8t$.

Step 2. Required answer.

The distance can be calculated as:

$$\begin{gathered} d=d_0+d_1+d_2+d_3+d_4+d_5+d_6+d_7 \\ =r_0{t}_0+r_1{t}_1+r_2{t}_2+r_3{t}_3+r_4{t}_4+r_5{t}_5+r_6{t}_6+r_7{t}_7 \\ =5v\left(0\right)+5v\left(5\right)+5v\left(10\right)+5v\left(15\right)+5v\left(20\right)+5v\left(25\right)+5v\left(30\right)+5v\left(35\right) \\ =0+192.5+330+412.5+440+412.5+330+192.5 \\ =2310 \end{gathered}$$