Math Problem Statement
The acceleration of a particle at time t is given by a(t) = ⟨t,et,sin(2t)⟩. Given that the velocity at t = 0 is equal to v(0) = ⟨1,1,1⟩ and the position at t = 0 is r(0) = ⟨0,0,0⟩ find the formula for the position vector r(t)
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Calculus
Integration
Kinematics
Formulas
v(t) = ∫a(t) dt
r(t) = ∫v(t) dt
Theorems
Fundamental Theorem of Calculus
Suitable Grade Level
Undergraduate Calculus
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