the graph shows the momentum y, in newton - seconds, of an object x seconds after the object started moving…

the graph shows the momentum y, in newton - seconds, of an object x seconds after the object started moving, for ( 0leq xleq8 ). what is the average rate of change, in newton - seconds per second, in the momentum of the object from ( x = 2 ) to ( x = 6 )?

the graph shows the momentum y, in newton - seconds, of an object x seconds after the object started moving, for ( 0leq xleq8 ). what is the average rate of change, in newton - seconds per second, in the momentum of the object from ( x = 2 ) to ( x = 6 )?

Answer

Explanation:

Step1: Identify the formula for average rate of change

The formula for the average rate of change of a function (y = f(x)) over the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}).

Step2: Determine the values of (f(a)) and (f(b))

From the graph, when (x = 2) (i.e., (a = 2)), (y=f(2)=6) (newton - seconds). When (x = 6) (i.e., (b = 6)), (y=f(6)=8) (newton - seconds).

Step3: Substitute into the formula

Substitute (a = 2), (b = 6), (f(a)=6), and (f(b)=8) into the formula (\frac{f(b)-f(a)}{b - a}). We get (\frac{8 - 6}{6-2}).

Step4: Simplify the expression

(\frac{8 - 6}{6 - 2}=\frac{2}{4}=\frac{1}{2})

Answer:

(\frac{1}{2})