step 2 of 2: if we ignore air resistance, a falling body will fall $16t^2$ feet in $t$ seconds. what is the average velocity between $t = 4$ and $t = 4.4$? round your answer to two decimal places if necessary.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Position and Velocity Relations" ], "new_concepts": [ "Average Velocity Calculation" ], "current_concepts": [ "Position and Velocity Relations", "Average Velocity Calculation" ] } ## Define the position function Using the *Position and Velocity Relations* knowledge point $$ s(t) = 16t^2 $$ ## Calculate position at the boundaries Using the *Position and Velocity Relations* knowledge point $$ \begin{aligned} s(4) &= 16(4)^2 = 16(16) = 256 \ s(4.4) &= 16(4.4)^2 = 16(19.36) = 309.76 \end{aligned} $$ ## Compute the average velocity Using the *Position and Velocity Relations* knowledge point $$ \begin{aligned} v_{\text{avg}} &= \frac{s(4.4) - s(4)}{4.4 - 4} \ v_{\text{avg}} &= \frac{309.76 - 256}{0.4} \ v_{\text{avg}} &= \frac{53.76}{0.4} = 134.4 \end{aligned} $$ If we ignore air resistance, a falling body will fall $16t^2$ feet in $t$ seconds. What is the average velocity between $t = 4$ and $t = 4.4$? Round your answer to two decimal places if necessary. 134.4 $ft/s$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Calculus", "Average Velocity Calculation" ] }

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Explanation:

Define the position function

Calculate position at the boundaries

Compute the average velocity

Answer: