AP Calculus BC Quiz
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PARAMETRIC, POLAR, AND VECTOR FUNCTIONS
Question 1
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A particle has velocity
v
⃗
(
t
)
=
⟨
2
t
,
cos
t
,
3
⟩
\vec v(t)=\langle 2t,\cos t,3\rangle
v
(
t
)
=
⟨
2
t
,
cos
t
,
3
⟩
and position
r
⃗
(
0
)
=
⟨
1
,
0
,
−
2
⟩
\vec r(0)=\langle 1,0,-2\rangle
r
(
0
)
=
⟨
1
,
0
,
−
2
⟩
; find
r
⃗
(
t
)
\vec r(t)
r
(
t
)
.
A
r
⃗
(
t
)
=
⟨
t
2
+
1
,
sin
t
,
−
2
+
3
t
⟩
\vec r(t)=\langle t^2+1,\sin t,-2+3t\rangle
r
(
t
)
=
⟨
t
2
+
1
,
sin
t
,
−
2
+
3
t
⟩
B
r
⃗
(
t
)
=
⟨
2
t
2
+
1
,
sin
t
,
−
2
+
3
t
⟩
\vec r(t)=\langle 2t^2+1,\sin t,-2+3t\rangle
r
(
t
)
=
⟨
2
t
2
+
1
,
sin
t
,
−
2
+
3
t
⟩
C
r
⃗
(
t
)
=
⟨
t
2
,
sin
t
,
−
2
+
3
t
⟩
\vec r(t)=\langle t^2,\sin t,-2+3t\rangle
r
(
t
)
=
⟨
t
2
,
sin
t
,
−
2
+
3
t
⟩
D
r
⃗
(
t
)
=
⟨
t
2
+
1
,
−
sin
t
,
−
2
+
3
t
⟩
\vec r(t)=\langle t^2+1,-\sin t,-2+3t\rangle
r
(
t
)
=
⟨
t
2
+
1
,
−
sin
t
,
−
2
+
3
t
⟩
E
r
⃗
(
t
)
=
⟨
t
2
+
1
,
sin
t
,
−
2
+
t
3
⟩
\vec r(t)=\langle t^2+1,\sin t,-2+t^3\rangle
r
(
t
)
=
⟨
t
2
+
1
,
sin
t
,
−
2
+
t
3
⟩
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