Math Problem Statement
1. A force F = 2i - yj, with x in meters, that acts on a particle as it moves from coordinates (-1,5) to (2,-4). What is the work done?
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Calculus
Work-Energy Theorem
Dot Product
Parametrization of Paths
Formulas
W = ∫ F · dr (Work done by a force over a displacement)
dr = dx i + dy j (Differential displacement in vector form)
Parametrization: x(t) = -1 + 3t, y(t) = 5 - 9t
Theorems
Work-Energy Theorem
Dot Product of Vectors
Suitable Grade Level
Undergraduate Level Physics/Mathematics
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