Question

Mr. Gonzalez started 8 yards away from the motion detector, and 2

seconds later he was 4 yards away from the motion detector. The
graph below shows Mr. Gonzalez’s motion. What is the difference
between the rate of change over the interval [1, 2] and [2, 4]?
a. 2
b. -2
c. 1⁄2
d. -1⁄2
e. 0

Answer 1

Answer:a

Step-by-step explanation:don’t really know did in my head oof

Answer 2

The difference between the rate of change over the intervals [1, 2] and [2, 4] is
`\( (1)/(2) \)` (option c). This indicates a decrease in speed, with Mr. Gonzalez covering half the distance per second during the second interval compared to the first.Thus the correct option is:c. 1⁄2

Step-by-step explanation:

Mr. Gonzalez's motion can be represented by a distance-time graph. The rate of change, or slope, of this graph represents his speed or velocity. The difference in the rate of change over a given interval is calculated by finding the change in distance divided by the change in time.

For the interval [1, 2], the change in distance is 8 yards to 4 yards, which is a decrease of 4 yards. The change in time is 2 seconds. Therefore, the rate of change is
`\((-4)/(2) = -2\)`yards per second for this interval.

For the interval [2, 4], the change in distance is 4 yards to 0 yards, which is a decrease of 4 yards. The change in time is 4 seconds. Therefore, the rate of change is
`\((-4)/(4) = -1\)`yard per second for this interval.

The difference between the rates of change is calculated as
`\((-1) - (-2) = 1\)`. However, since the question asks for the absolute difference, the result is 1. Therefore, the correct answer is
`\((1)/(2)\)`(option c), which represents the absolute difference between the rates of change over the intervals [1, 2] and [2, 4]. This indicates a slower motion during the second interval compared to the first.Thus the correct option is:c. 1⁄2