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Mathematics
Problem
For a differentiable velocity function
v
(
t
)
v(t)
v
(
t
)
, which of the following expressions gives the particle’s average velocity on the time interval
[
a
,
b
]
[a,b]
[
a
,
b
]
with
a
<
b
a<b
a
<
b
? a)
v
(
b
)
−
v
(
a
)
b
−
a
\displaystyle \frac{v(b)-v(a)}{b-a}
b
−
a
v
(
b
)
−
v
(
a
)
b)
∫
a
b
v
(
t
)
d
t
\displaystyle \int_{a}^{b} v(t)\,dt
∫
a
b
v
(
t
)
d
t
c)
1
b
−
a
∫
a
b
v
(
t
)
d
t
\displaystyle \frac{1}{b-a}\int_{a}^{b} v(t)\,dt
b
−
a
1
∫
a
b
v
(
t
)
d
t
d)
1
b
−
a
∫
a
b
∣
v
(
t
)
∣
d
t
\displaystyle \frac{1}{b-a}\int_{a}^{b} |v(t)|\,dt
b
−
a
1
∫
a
b
∣
v
(
t
)
∣
d
t
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