Exercício de Dinamica (78)

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89 
 
PROBLEM 11.64 
A particle moves in a straight line with the 
velocity shown in the figure. Knowing that 
540 mx = − at t = 0, (a) construct the a t− and 
x t− curves for 0 50 s,t< < and determine (b) 
the maximum value of the position coordinate of 
the particle, (c) the values of t for which the 
particle is at 100 m.x = 
 
SOLUTION 
(a) slope of ta v t= − curve at time t 
 From 0t = to 10 s:t = constant 0v a=  = 
 10 st = to 26 s:t = 220 60
5 m/s
26 10
a
− −= = −
−
 
 26 st = to 41s:t = constant 0v a=  = 
 41st = to 46 s:t = 25 ( 20)
3 m/s
46 41
a
− − −= =
−
 
 46 s:t = constant 0v a=  = 
 
 2 1x x= + (area under v t− curve from 1t to 2 )t 
 At 10 s:t = 10 540 10(60) 60 mx = − + = 
 Next, find time at which 0.v = Using similar triangles 
 0
0
10 26 10
or 22 s
60 80
v
v
t
t=
=
− −= = 
 At 22
26
41
46
50
1
22 s: 60 (12)(60) 420 m
2
1
26 s: 420 (4)(20) 380 m
2
41s: 380 15(20) 80 m
20 5
46 s: 80 5 17.5 m
2
50 s: 17.5 4(5) 2.5 m
t x
t x
t x
t x
t x
= = + =
= = − =
= = − =
+ = = − = 
 
= = − = −