In quadrant 1: The curve begins at point (0 comma 1). The curve rises sharply to point (2 comma 6).

Question

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 $x equals 6$ ?

Accepted Answer

The correct answer is 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 = 2 , the corresponding y -value is 6 . The graph also shows that at x = 6 , the corresponding y -value is 8 . It follows that the average rate of change, in newton-seconds per second, from x = 2 to x = 6 is 8 - 6 6 - 2 , which is equivalent to 2 4 , or 1 2 . Note that 1/2 and .5 are examples of ways to enter a correct answer.

Question in-qua