TD Physique : Exercice 13 page 18
MRUA, rappels :
Loi des espaces :
2
².
00
ta
tvxx +⋅+= ; Loi des vitesses :
tavv ⋅+= 0
; Accélération = c
ste
Manœuvre 1
:
MRUA
t = 5,0 s
a = 2,0 m/s²
v = ?
→
0 + 2,0.5,0 = 10 m/s
x = ?
→
0 + 0 + 2,0.5,0²/2 = 25 m
x
t
= 25 m
Manœuvre 2
:
MRU
t = ?
→
30,0 m à 10 m/s
→
30,0 / 10 = 3,0 s
a = 0 m/s²
v = 10 m/s
x = 0 + 10,0.3,0 + 0 = 30 m
x
t
= 25 + 30 = 55 m
Manœuvre 3 :
t = 2,0 s
a = ?
→
tavv ⋅+= 0
→
0 = 10,0 + a.2,0
→
a = - 5,0 m/s²
v = 0,0 m/s
x = ?
→
2
².
00 ta
tvxx +⋅+=
→
x = 0 + 10,0.2,0 + (-5,0).2,0²/2
→
x = 10 m
x
t
= 55 + 10 = 65 m
Manœuvre 4 :
t = 3 s
a = 0 m/s²
v = 0 m/s
x = 0 m
x
t
= 65 + 0 = 65 m
Manœuvre 5 :
t = 2,0 s
a = ?
→
-5,0 = 0 + 0 + a.2,0²/2
→
a = - 2,5 m/s²
v = ?
→
v = 0 + (-2,5).2,0
→
-5,0 m/s
x = - 5,0 m
x
t
= 65 – 5 = 60 m
Manœuvre 6 :
t = ?
→
-20,0 = 0 + (-5,0).t
→
t = 4,0 s car a = 0
a = 0 m/s²
v = - 5,0 m/s
x = - 20,0 m
x
t
60 – 20 = 40 m
Manœuvre 7 :
t = 4,0 s
a = ?
→
0 = -5,0 + a.4,0
→
a = 1,25 m/s²
v = 0 m/s
x = ?
→
x = 0 + (-5,0).4,0 + 1,25.4,0²/2 = -10 m
x
t
40 - 10 = 30 m
Manœuvre 8:
t = 2,0 s
a = 0 m/s²
v = 0 m/s
x = 0 m
x
t
= 30 - 0 = 30 m
A terminer : Graphiques de la position, de la vitesse et de l’accélération en fonction du temps.
x
t
v
t
a
t
25
55
10
2
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