fisica1-youn-e-freedman-exercicios-resolvidos

4.57: In this situation, the x-component of force depends explicitly on the y-component of
position. As the y-component of force is given as an explicit function of time, v
y
and y
can be found as functions of time. Specifically,
3
3
/ 6m)
2
a y
= k / m)
t , so v y
= ( k / 2m
t and
( 3
3
)
y = ( k t , where the initial conditions v y
= , y 0 have been used. Then, the
expressions for
In vector form,
x
x
0
0 0
=
a , v and x are obtained as functions of time:
k1
k2k3
3
ax
= + t
2
m 6m
k1
k2k3
vx
= t + t
2
m 24m
k1
2 k2k3
x = t +
2m
120m
r ⎛ k1
2 k2k3
= ⎜ t + t
2
⎝ 2m
120m
r ⎛ k1
k2k3
v = ⎜ t + t
2
⎝ m 24m
5
4
4
2
t
5
.
⎞ ˆ ⎛ k3
⎟i
+ ⎜ t
⎠ ⎝ 6m
⎞ ˆ ⎛ k3
⎟i
+ ⎜ t
⎠ ⎝ 2m
⎞
⎟ ˆj
⎠
3
2
⎞
⎟ ˆ. j
⎠