If an arrow is shot upward on the moon with a speed of 58 m/s, its height in meters t seconds...

Question:

If an arrow is shot upward on the moon with a speed of 58 m/s, its height in meters {eq}t {/eq} seconds later is given by {eq}y = 58t - 0.83t^2 {/eq}. (Round your answers to two decimal places.)

(a) Find the average speed over the given time intervals.

(i) {eq}[1, 2] {/eq}

(ii) {eq}[1,1.5] {/eq}

(iii) {eq}[1,1.1] {/eq}

(iv) {eq}[1,1.01] {/eq}

(v) {eq}[1,1.001] {/eq}

(b) Estimate the speed when {eq}t = 1 {/eq}.

Average Rate of Change

In order to find the average rate of change of a function, we're looking for the rate of change of a function between two points. This is the same as finding the slope between these two points, as we're finding the ratio of the change in the function over the change in {eq}x {/eq}.

$$\frac{f(b) - f(a)}{b-a}$$

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a) To find the average speed over the intervals given, we need to find the average rates of change. This is because the velocity of a position... Average Rate of Change: Definition, Formula & Examples

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Chapter 20 / Lesson 5
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Finding the average rate of change is similar to finding the slope of a line. Study the definition of average rate of change, its formula, and examples of this concept.