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USA Physics and Chemistry Contests
F = Ma
2007 F = Ma
1
1
Part of
2007 F = Ma
Problems
(1)
2007 F = ma #1: Position Vector
Source:
11/16/2012
An object moves in two dimensions according to
r
⃗
(
t
)
=
(
4.0
t
2
−
9.0
)
i
⃗
+
(
2.0
t
−
5.0
)
j
⃗
\vec{r}(t) = (4.0t^2 - 9.0)\vec{i} + (2.0t - 5.0)\vec{j}
r
(
t
)
=
(
4.0
t
2
−
9.0
)
i
+
(
2.0
t
−
5.0
)
j
where
r
r
r
is in meters and
t
t
t
in seconds. When does the object cross the
x
x
x
-axis?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
0.0
s
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
0.4
s
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
0.6
s
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
1.5
s
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
2.5
s
<span class='latex-bold'>(A)</span>\ 0.0 \text{ s}\qquad<span class='latex-bold'>(B)</span>\ 0.4 \text{ s}\qquad<span class='latex-bold'>(C)</span>\ 0.6 \text{ s}\qquad<span class='latex-bold'>(D)</span>\ 1.5 \text{ s}\qquad<span class='latex-bold'>(E)</span>\ 2.5 \text{ s}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
0.0
s
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
0.4
s
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
0.6
s
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
1.5
s
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
2.5
s
vector
analytic geometry