Exercício de Dinamica (87)

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98 
= Δx = 6 m 
 
 
PROBLEM 11.70 
The acceleration record shown was obtained for a small 
airplane traveling along a straight course. Knowing that x = 0 
and 60 m/sv = when 0,t = determine (a) the velocity and 
position of the plane at 20 s,t = (b) its average velocity 
during the interval 6 s 14 s.t< < 
 
SOLUTION 
 
Geometry of “bell-shaped” portion of v t− curve 
 
The parabolic spandrels marked by * are of equal area. Thus, total area of shaded portion of v t− diagram is: 
 
 
(a) When 20 s:t = 20 60 m/sv =  
 20 (60 m/s) (20 s) (shaded area)x = − 
 1200 m 6 m= − 20 1194 mx =  
(b) From 6 s to 14 s: 8 st t t= = Δ = 
 
(60 m/s)(14 s 6 s) (shaded area)
(60 m/s)(8 s) 6 m 480 m 6 m 474 m
xΔ = − −
= − = − =
 
 average
474 m
8 s
x
v
t
Δ= =
Δ
 average 59.25 m/sv = 