Math Problem Statement

The displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation s = 4 sin(𝜋t) + 3 cos(𝜋t), where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the average velocity during each time period. (i) [1, 2]

[1, 1.01]

cm/s (iv) [1, 1.001]

Solution

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Kinematics
Average Velocity

Formulas

Average velocity = (s(t2) - s(t1)) / (t2 - t1)
Displacement function: s(t) = 4 sin(πt) + 3 cos(πt)

Theorems

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Suitable Grade Level

Grades 10-12