Read Example 2.2 in the textbook
Links to an external site.
.

An object moves along a coordinate axis so that its position at time
𝑡
is given by
𝑠
(
𝑡
)
=
5
ln
⁡
𝑡
. Find its average velocity over the time interval
[
1.5
,
1.7
]
.

Round your answer to 4 decimal places. (You may use a calculator.)

Question

Read Example 2.2 in the textbook
Links to an external site.
.

An object moves along a coordinate axis so that its position at time 
𝑡
 is given by 
𝑠
(
𝑡
)
=
5
ln
⁡
𝑡
 . Find its average velocity over the time interval 
[
1.5
,
1.7
]
 .

Round your answer to 4 decimal places. (You may use a calculator.)

BlackTom AI · Accepted Answer

The problem asks for the average velocity of a particle whose position is given by s(t) = 5 ln t over the interval [1.5, 1.7], rounded to four decimals.

First, recall that average velocity on an interval [a, b] is defined as [s(b) − s(a)] / (b − a).

Compute s(1.7):
- s(1.7) = 5 ln(1.7).
- The natural logarithm of 1.7 is approximately 0.5306282515, so s(1.7) ≈ 5 × 0.5306282515 ≈ 2.6531412575.

Compute s(1.5):
- s(1.5) = 5 ln(1.5).
- The natural logarithm of 1.5 is approximately 0.4054651081, so s(1.5) ≈ 5 × 0.4054651081 ≈ 2.0273255405.

Difference in position:
- s(1.7) − s(1.5) ≈ 2.6531412575 − 2.0273255405 ≈ 0.6258157170.

Difference in time:
- 1.7 − 1.5 = 0.2.

Average velocity:
- (s(1.7) − s(1.5)) / (1.7 − 1.5) ≈ 0.6258157170 / 0.2 ≈ 3.129078585.

Rounding to four decimal places:
- 3.1291.

Notes on the provided answer:
- The value given in the dataset is 2.8555. This does not match the calculation above based on s(t) = 5 ln t and the standard average-velocity formula. It may reflect a misprint, a different interpretation, or an error in the supplied answer key. When performing the calculation step by step with the stated s(t) and interval, the result consistently rounds to 3.1291, not 2.8555.

If you are instructed to use the supplied answer 2.8555, you should double-check the exact form of s(t) (for example, whether a constant term or a different function is used) and whether the interval endpoints or rounding requirements differ from the stated problem. Otherwise, applying the standard formula yields 3.1291 as the correct average velocity for s(t) = 5 ln t on [1.5, 1.7].

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