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Mathematics
Problem
A particle moves in the plane with position vector
r
(
t
)
\mathbf r(t)
r
(
t
)
and velocity vector
v
(
t
)
=
r
′
(
t
)
\mathbf v(t)=\mathbf r'(t)
v
(
t
)
=
r
′
(
t
)
. Which of the following expressions gives the particle’s net displacement vector from
t
=
2
t=2
t
=
2
to
t
=
5
t=5
t
=
5
? a)
3
v
(
5
)
3\,\mathbf v(5)
3
v
(
5
)
b)
∫
2
5
v
(
t
)
d
t
\displaystyle\int_{2}^{5}\mathbf v(t)\,dt
∫
2
5
v
(
t
)
d
t
c)
r
(
5
)
+
r
(
2
)
2
\displaystyle\frac{\mathbf r(5)+\mathbf r(2)}{2}
2
r
(
5
)
+
r
(
2
)
d)
r
(
5
)
+
r
(
2
)
\mathbf r(5)+\mathbf r(2)
r
(
5
)
+
r
(
2
)
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