Math Problem Statement
Find the velocity, acceleration, and speed of a particle with position function r(t) = ⟨et, cos(πt), ln(t)⟩ at t = 2.
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Calculus
Derivatives
Velocity
Acceleration
Speed
Formulas
Velocity: v(t) = dr(t)/dt = ⟨d/dt e^t, d/dt cos(πt), d/dt ln(t)⟩
Acceleration: a(t) = dv(t)/dt = ⟨d/dt e^t, d/dt (-π sin(πt)), d/dt (1/t)⟩
Speed: |v(t)| = sqrt(v1^2 + v2^2 + v3^2)
Theorems
Fundamental Theorem of Calculus
Chain Rule for Derivatives
Suitable Grade Level
Undergraduate (Calculus II or III)
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