Question

non_et_al_Fundamentals_of_fluid_ Mecha.pdf (page 210 of 818) *4.15 A test car is traveling along a level road at 88 km/hr. In order to study the acceleration characteristics of a newly installed engine, the car accelerates at its maximum possible rate. The test crew records the following velocities at various locations along the level road: x = 0 V = 88.5 km/hr x = 0.1 km V = 93.1 km/hr x = 0.2 km V = 98.3 km/hr x = 0.3 km V = 104.0 km/hr x = 0.4 km V = 110.3 km/hr x = 0.5 km V = 117.2 km/hr x = 1.0 km V = 164.5 km/hr. A preliminary study shows that these data follow an equation of the form V = A(1 + EB), where A and B are positive constants. Find A and B and a Lagrangian expression V = V(V, 1), where V, is the car velocity at time 1 = 0) when x = 0.

Answer 1

distance N=0 a=Oil km N=0r2 km U=0r3 km n=0.14 km X=0,5 cm n=100 km velocity V=8815 Km/hr V=9311 km/hr v=98.3 km/hr v=104.0 km/hr v=11013 cm Ihr v=11702 km/hr v=164.5 km/hr velocity, VEACited) - now, A B. at, dao, v=vo= 88.5 km/br. N=1 , v= 16405 km/hr at, no v=vo= 88.5 Km/hr v=A[ite BM) A No 88.5 - 4425 2 No= (1 + e) A TA= 44.25 No =

at, x=2, v= 16415 km/hr. v= A(lte B 1641 5= 44.29(1+0) 18415 - 1 te B e BE 16:45 B = 3 3,7175-19 B = 2,7175 A=44125 B= ln (217175) B = 0.gg Now, Lagrangian 2 = 7-9 2 2= 2 m v zv 2 y potential energy