Answer
a) $5220$ meters
b) $5520$ meters
Work Step by Step
a. Using left-endpoint values:
For the subinterval [0, 5], velocity = 1
For the subinterval [5, 10], velocity = 1.2
For the subinterval [10, 15], velocity = 1.7
For the subinterval [15, 20], velocity = 2.0
For the subinterval [20, 25], velocity = 1.8
For the subinterval [25, 30], velocity = 1.6
For the subinterval [30, 35], velocity = 1.4
For the subinterval [35, 40], velocity = 1.2
For the subinterval [40, 45], velocity = 1.0
For the subinterval [45, 50], velocity = 1.8
For the subinterval [50, 55], velocity = 1.5
For the subinterval [55, 60], velocity = 1.2
Now, let's calculate the areas of the rectangles and sum them up:
Area = (5) $\times$ 1 + (5) $\times$ 1.2 + (5) $\times$ 1.7 + (5) $\times$ 2.0 + (5) $\times$ 1.8 + (5) $\times$ 1.6 + (5) $\times$ 1.4 + (5) $\times$ 1.2 + (5) $\times$ 1.0 + (5) $\times$ 1.8 + (5) $\times$ 1.5 + (5) $\times$ 1.2
= 5 + 6 + 8.5 + 10 + 9 + 8 + 7 + 6 + 5 + 9 + 7.5 + 6
= 87 m per 5 minutes = $\frac{87\times300}{5}$ =5220 meters.
b. Using right-endpoint values:
For the subinterval [0, 5], velocity = 1.2
For the subinterval [5, 10], velocity = 1.7
For the subinterval [10, 15], velocity = 2.0
For the subinterval [15, 20], velocity = 1.8
For the subinterval [20, 25], velocity = 1.6
For the subinterval [25, 30], velocity = 1.4
For the subinterval [30, 35], velocity = 1.2
For the subinterval [35, 40], velocity = 1.0
For the subinterval [40, 45], velocity = 1.8
For the subinterval [45, 50], velocity = 1.5
For the subinterval [50, 55], velocity = 1.2
For the subinterval [55, 60], velocity = 0 m/s
Now, let's calculate the areas of the rectangles and sum them up:
Area = (5) $\times$ 1.2 + (5) $\times$ 1.7 + (5) $\times$ 2.0 + (5) $\times$ 1.8 + (5) $\times$ 1.6 + (5) $\times$ 1.4 + (5) $\times$ 1.2 + (5) $\times$ 1.0 + (5) $\times$ 1.8 + (5) $\times$ 1.5 + (5) $\times$ 1.2 + (5) $\times$ 0
= 6 + 8.5 + 10 + 9 + 8 + 7 + 6 + 5 + 9 + 7.5 + 6 + 0
= 92 m per 5 minutes = $\frac{92\times300}{5}$ =5520 meters.
