Q. 53

Question

Considering the stoplight example in the reading with velocity $v (t) = - 0.22 t^{2} + 8.8 t$ 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 $v (t)$ .

Step-by-Step Solution

Verified

Answer

The distance is $2310 f e e t .$

1Step 1. Given information.

The given function is $v (t) = - 0.22 t^{2} + 8.8 t$ .

2Step 2. Required answer.

The distance can be calculated as:

$d = d_{0} + d_{1} + d_{2} + d_{3} + d_{4} + d_{5} + d_{6} + d_{7} = r_{0} t_{0} + r_{1} t_{1} + r_{2} t_{2} + r_{3} t_{3} + r_{4} t_{4} + r_{5} t_{5} + r_{6} t_{6} + r_{7} t_{7} = 5 v (0) + 5 v (5) + 5 v (10) + 5 v (15) + 5 v (20) + 5 v (25) + 5 v (30) + 5 v (35) = 0 + 192.5 + 330 + 412.5 + 440 + 412.5 + 330 + 192.5 = 2310$

Q. 52

Q. 54

Other exercises in this chapter

Q. 51

Determine which of the limit of sums in Exercises 47–52 are infinite and which are finite. For each limit of sums that is finite, compute its value

View solution

Q. 52

Determine which of the limit of sums in Exercises 47–52 are infinite and which are finite. For each limit of sums that is finite, compute its value

View solution

Q. 54

Suppose you drive on a racetrack for 10 minutes with velocity as shown in the graph&#

View solution

Q. 55

The table that follows describes the activity in a college tuition savings account over fo

View solution