Math Problem Statement
A 10kg body falls from rest. If air resistance is proportional to speed, and if the limiting speed is 50 meter per second. Find the speed at the end of 5 seconds
Solution
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Math Problem Analysis
Mathematical Concepts
Differential Equations
Forces in Physics
Exponential Decay
Formulas
mg = kv_lim (force balance for terminal velocity)
m dv/dt = mg - kv (equation of motion with air resistance)
v = v_lim * (1 - e^(-kt/m)) (velocity solution with air resistance)
Theorems
Separable Differential Equations
Exponential Decay Law
Suitable Grade Level
Grades 11-12 (Advanced Physics/Calculus Level)