fisica1-youn-e-freedman-exercicios-resolvidos

2.51: a) From Eqs. (2.17) and (2.18), with v 0 =0 and x 0 =0,
v
x
= ∫
t ⎛ A
x = ∫ ⎜ t
0
⎝ 2
B
3
B
− t
12
t
2
2 2
3 3
4 3
( At − Bt ) dt = t − t = (0.75 m s ) t − (0.040 m s ) t
0
2
B
− t
3
3
A
2
⎞
⎟ dt =
⎠
A
t
6
3
4
3 3
= (0.25 m s ) t
4 4
− (0.010 m s ) t .
b) For the velocity to be a maximum, the acceleration must be zero; this occurs at t=0
A
and t = B
=12.5 s . At t=0 the velocity is a minimum, and at t=12.5 s the velocity is
v
x
= (0.75 m
s
3
)(12.5 s)
2
− (0.040
m
s
4
)(12.5s)
3
= 39.1 m s.