Exercício de Dinamica (113)

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124 
 
 
PROBLEM 11.87 
The acceleration of an object subjected to the pressure wave of a 
large explosion is defined approximately by the curve shown. The 
object is initially at rest and is again at rest at time t1. Using the 
method of section 11.8, determine (a) the time t1, (b) the distance 
through which the object is moved by the pressure wave. 
 
SOLUTION 
 
 
(a) Since 0v = when 0t = and when 1t t= the change in v between 0t = and 1t t= is zero. 
 Thus, area under a−t curve is zero 
 
1 2 3
1
1
0
1 1 1
(30)(0.6) ( 10)(0.2) ( 10)( 0.8) 0
2 2 2
9 1 5 4 0
A A A
t
t
+ + =
+ − + − − =
− − + = 1 2.40 st =  
(b) Position when t = t1 = 2.4 s 
 
0 0 1 1 1 2 1 3 1
2
( 0.2) ( 0.733) ( 0.8)
3
1 2
0 0 (9)(2.4 0.2) ( 1)(2.4 0.733) ( 10)(2.4 0.8) (2.4 0.8)
2 3
19.8 m 1.667 m 8.533 m
x x v t A t A t A t
 = + + − + − + − 
 
 = + + − + − − + − − −  
= − − 9.60 mx = 