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The table shows the position of a motorcyclist after accelerating from rest. t ssecondsd
Chapter 2, Problem 7(choose chapter or problem)
The table shows the position of a motorcyclist after accelerating from rest.
\(\begin{array}{|l|c|c|c|c|c|c|c|} \hline t \text { (seconds) } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline s \text { (feet) } & 0 & 4.9 & 20.6 & 46.5 & 79.2 & 124.8 & 176.7 \\ \hline \end{array}\)
(a) Find the average velocity for each time period:
\(\begin{array}{l}\text{(i) } [2,4]\\ \text{(ii) } [3,4]\\ \text{(iii) } [4,5]\\ \text{(iv) } [4,6]\end{array}\)
(b) Use the graph of s as a function of t to estimate the instantaneous velocity when \(t=3\).
Questions & Answers
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QUESTION:
The table shows the position of a motorcyclist after accelerating from rest.
\(\begin{array}{|l|c|c|c|c|c|c|c|} \hline t \text { (seconds) } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline s \text { (feet) } & 0 & 4.9 & 20.6 & 46.5 & 79.2 & 124.8 & 176.7 \\ \hline \end{array}\)
(a) Find the average velocity for each time period:
\(\begin{array}{l}\text{(i) } [2,4]\\ \text{(ii) } [3,4]\\ \text{(iii) } [4,5]\\ \text{(iv) } [4,6]\end{array}\)
(b) Use the graph of s as a function of t to estimate the instantaneous velocity when \(t=3\).
ANSWER:
Step 1 of 10
Consider the data for the position of a motorcyclist after accelerating from rest.
\(\begin{array}{|l|c|c|c|c|c|c|c|} \hline t \text { (seconds) } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline s \text { (feet) } & 0 & 4.9 & 20.6 & 46.5 & 79.2 & 124.8 & 176.7 \\ \hline \end{array}\)
(a) The objective is to find the average velocity for the time period [2,4],.
(i) Observe from the table,
At \(t=2\),the position \(s(2)=20.6\)
At \(t=4\),the position \(s(4)=79.2\)
The average velocity is ,
\(\begin{array}{l} \text { Average velocity }=\frac{\text { change in position }}{\text { time elapsed }} \\ =\frac{s(4)-s(2)}{4-2} \\ =\frac{79.2-20.6}{2} \\ =\frac{58.6}{2} \\ =29.3 \end{array}\)
Therefore the average velocity for the time period [2,4] is 29.3 feet/second.
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