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Vehicle Model: Analytical Solution tw -FDrag FTract N F frict dv Σε F = ma m Ftract FFrict - Fdrag dt FFrict HN μmg 1 Farag = PCaAv² 1 FT - HRmg - PCDAv² dv m = dt dv m =a- bv² dt If we neglect Ftract - FFrict, we will have: dv dt m = -bv² Then you can solve the integration: mf-bf dt (do it by yourself) v(t) = fv (vo,t)

Vehicle Model: Analytical Solution tw -FDrag FTract N F frict dv Σε F = ma m Ftract FFrict - Fdrag dt FFrict HN μmg 1 Farag = PCaAv² 1 FT - HRmg - PCDAv² dv m = dt dv m =a- bv² dt If we neglect Ftract - FFrict, we will have: dv dt m = -bv² Then you can solve the integration: mf-bf dt (do it by yourself) v(t) = fv (vo,t)

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Solve the integration for the analytical solution problem.
Vehicle Model: Analytical Solution t W Forag F-Tract N frict dv Σε F = ma m. = Ftract FFrict - Fdrag dt FFrict 1 Nμμmg Farag = pCaAv² dv m dt = FT-μŔmg - PCDAV² dv m = a - bv² dt If we neglect Ftract - FFrict, we will have: dv dt m- = -bv² Then you can solve the integration: dv m =-bf dt (do it by yourself) v(t) = fv (vo, t) Vehicle Model: Analytical Solution tw If we neglect Ftract - FFrict, we will have: m dv = -bv² dt Then you can solve the integration: =-bf dt (do it by yourself) -FDrag m Tract N frict 1. To analyze the traveling distance (assume initial position is xo): dx dt · = v(t) = fv (vo, t) (do integration by yourself) x(t) = fx (x,t) 2. When will the car stop: v(t) = f (vo,t) = 0
Transcribed Image Text:Vehicle Model: Analytical Solution t W Forag F-Tract N frict dv Σε F = ma m. = Ftract FFrict - Fdrag dt FFrict 1 Nμμmg Farag = pCaAv² dv m dt = FT-μŔmg - PCDAV² dv m = a - bv² dt If we neglect Ftract - FFrict, we will have: dv dt m- = -bv² Then you can solve the integration: dv m =-bf dt (do it by yourself) v(t) = fv (vo, t) Vehicle Model: Analytical Solution tw If we neglect Ftract - FFrict, we will have: m dv = -bv² dt Then you can solve the integration: =-bf dt (do it by yourself) -FDrag m Tract N frict 1. To analyze the traveling distance (assume initial position is xo): dx dt · = v(t) = fv (vo, t) (do integration by yourself) x(t) = fx (x,t) 2. When will the car stop: v(t) = f (vo,t) = 0
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