Examples 7 A particle moves in a straight line with a constant acceleration of -4 ft/s2 for 6 s, zero acceleration for the next 4 s, and a constant acceleration of +4 ft/s2 for the next 4 s. Knowing that the particle starts from the origin and that its velocity is -8 ft/s during the zero-acceleration time interval, (a) construct the v-t and x-t curves for 0 st s 14 s, (b) determine the position and the velocity of the particle and the total distance traveled when t = 14 s. a (ft/s²) 4 SOLUTION 6 0 10 14 t(s) -4 12 From the a- curve (a) Construct the v-1 curve: From the v-curve (b) Construct the x-1 curve 4-24 ft/s, 4, 16 ft/s --8 ft/s V₁ = V6-4 =-8-(-24) = 16 ft/s Vio=-8 ft/s 14 = 10 +42 =-8+16 = 8 ft/s = 4 32 ft, 4-8 ft As -32 ft, 4-8 ft, 4, 8 ft x=0 x4x+y=32 ft a (A/8") 4 16 ft/s ° t(s) A--24% √(ft/s) 16 8 ° x=x+4=24 ft 10 A-8 ft 1210A-16 ft 1412A-8 ft x (ft) ཟླ༥༠༡ d₁ =|32-0-32 ft d₂-|-16-32-48 ft Total Distance Traveled 4s ≤1 ≤ 12s, 12 s sr≤ 14 s d = 32 +48 +8 8-(-)-8-|- t() d = 88 ft 12
Examples 7 A particle moves in a straight line with a constant acceleration of -4 ft/s2 for 6 s, zero acceleration for the next 4 s, and a constant acceleration of +4 ft/s2 for the next 4 s. Knowing that the particle starts from the origin and that its velocity is -8 ft/s during the zero-acceleration time interval, (a) construct the v-t and x-t curves for 0 st s 14 s, (b) determine the position and the velocity of the particle and the total distance traveled when t = 14 s. a (ft/s²) 4 SOLUTION 6 0 10 14 t(s) -4 12 From the a- curve (a) Construct the v-1 curve: From the v-curve (b) Construct the x-1 curve 4-24 ft/s, 4, 16 ft/s --8 ft/s V₁ = V6-4 =-8-(-24) = 16 ft/s Vio=-8 ft/s 14 = 10 +42 =-8+16 = 8 ft/s = 4 32 ft, 4-8 ft As -32 ft, 4-8 ft, 4, 8 ft x=0 x4x+y=32 ft a (A/8") 4 16 ft/s ° t(s) A--24% √(ft/s) 16 8 ° x=x+4=24 ft 10 A-8 ft 1210A-16 ft 1412A-8 ft x (ft) ཟླ༥༠༡ d₁ =|32-0-32 ft d₂-|-16-32-48 ft Total Distance Traveled 4s ≤1 ≤ 12s, 12 s sr≤ 14 s d = 32 +48 +8 8-(-)-8-|- t() d = 88 ft 12
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter1: Introduction To Statics
Section: Chapter Questions
Problem 1.19P: Plot the earths gravitational acceleration g(m/s2) against the height h (km) above the surface of...
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Transcribed Image Text:Examples 7
A particle moves in a straight line with a constant acceleration of -4 ft/s2 for 6 s, zero
acceleration for the next 4 s, and a constant acceleration of +4 ft/s2 for the next 4 s. Knowing
that the particle starts from the origin and that its velocity is -8 ft/s during the zero-acceleration
time interval, (a) construct the v-t and x-t curves for 0 st s 14 s, (b) determine the position
and the velocity of the particle and the total distance traveled when t = 14 s.
a (ft/s²)
4
SOLUTION
6
0
10
14
t(s)
-4
12
From the a- curve
(a) Construct the v-1 curve:
From the v-curve
(b) Construct the x-1 curve
4-24 ft/s, 4, 16 ft/s
--8 ft/s
V₁ = V6-4
=-8-(-24)
= 16 ft/s
Vio=-8 ft/s
14 = 10 +42
=-8+16
= 8 ft/s
=
4 32 ft, 4-8 ft
As -32 ft, 4-8 ft, 4, 8 ft
x=0
x4x+y=32 ft
a (A/8")
4
16 ft/s
°
t(s)
A--24%
√(ft/s)
16
8
°
x=x+4=24 ft
10 A-8 ft
1210A-16 ft
1412A-8 ft
x (ft)
ཟླ༥༠༡
d₁ =|32-0-32 ft
d₂-|-16-32-48 ft
Total Distance Traveled
4s ≤1 ≤ 12s,
12 s sr≤ 14 s
d = 32 +48 +8
8-(-)-8-|-
t()
d = 88 ft
12
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