sat suite question viewer

Problem-Solving and Data Analysis / Two-variable data: Models and scatterplots Difficulty: Medium

The graph shows the momentum $y$ , in newton-seconds, of an object $x$ seconds after the object started moving, for $0 \leq x \leq 8$ . What is the average rate of change, in newton-seconds per second, in the momentum of the object from $x equals 2$ to $x equals 6$ ?

Back question 7 of 63 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63

Explanation

The correct answer is $\frac{1}{2}$ . For the graph shown, $x$ represents time, in seconds, and $y$ represents momentum, in newton-seconds. Therefore, the average rate of change, in newton-seconds per second, in the momentum of the object between two x-values is the difference in the corresponding y-values divided by the difference in the x-values. The graph shows that at $x equals 2$ , the corresponding y-value is $6$ . The graph also shows that at $x equals 6$ , the corresponding y-value is $8$ . It follows that the average rate of change, in newton-seconds per second, from $x equals 2$ to $x equals 6$ is $\frac{8 - 6}{6 - 2}$ , which is equivalent to $\frac{2}{4}$ , or $\frac{1}{2}$ . Note that 1/2 and .5 are examples of ways to enter a correct answer.