Question

name:date:average rate of change and motionn-gen math® algebra i homeworkfluency1. an object moves such that the total distance it has traveled is given as a function of time in the table below:| time (seconds) | 0 | 2 | 5 | 7 | 8 | 12 | 15 || ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- || distance (feet) | 0 | 7 | 22 | 31 | 37 | 45 | 48 |calculate the average speed the object is moving over each of the following intervals. include proper units in your answer.(a) from 0 to 15 seconds(b) from 5 to 8 seconds(c) from 7 to 12 seconds2. using the table above, is the object moving faster on average from 2 to 5 seconds or from 7 to 8 seconds? justify your answer with evidence.

Explanation:

Step1: Define average speed formula

Average speed = $\frac{\text{Change in Distance}}{\text{Change in Time}}$

Step2: Calculate (a) 0 to 15 seconds

Change in distance: $48 - 0 = 48$ feet
Change in time: $15 - 0 = 15$ seconds
Expression: $\frac{48}{15} = 3.2$ feet/second

Step3: Calculate (b) 5 to 8 seconds

Change in distance: $37 - 22 = 15$ feet
Change in time: $8 - 5 = 3$ seconds
Expression: $\frac{15}{3} = 5$ feet/second

Step4: Calculate (c) 7 to 12 seconds

Change in distance: $45 - 31 = 14$ feet
Change in time: $12 - 7 = 5$ seconds
Expression: $\frac{14}{5} = 2.8$ feet/second

Step5: Compare 2-5 and 7-8 intervals

First, calculate 2 to 5 seconds:
Change in distance: $22 - 7 = 15$ feet
Change in time: $5 - 2 = 3$ seconds
Expression: $\frac{15}{3} = 5$ feet/second
Then compare to 7-8 seconds (already found as 6 feet/second, calculated as $\frac{37-31}{8-7}=6$ feet/second)

Answer:

1. (a) 3.2 feet per second

(b) 5 feet per second
(c) 2.8 feet per second

1. The object moves faster on average from 7 to 8 seconds. The average speed from 2 to 5 seconds is 5 feet/second, while the average speed from 7 to 8 seconds is 6 feet/second, and 6 > 5.