Questions: The table shows the position of a motorcyclist after accelerating from rest. t (seconds) 0 1 2 3 4 5 6 s (feet) 0 4.9 10.6 23.1 50.2 109.3 237.9 (a) Find the average velocity (in ft/s) for each time period. (i) [2,4] (ii) [3,4] (iii) [4,5] (iv) [4,6] (b) Plot the points in the table to create a graph of s as a function of t to estimate the instantaneous velocity (in ft/s) when t=3. (Round your answer to one decimal place.)

The table shows the position of a motorcyclist after accelerating from rest. t (seconds) 0 1 2 3 4 5 6 s (feet) 0 4.9 10.6 23.1 50.2 109.3 237.9 (a) Find the average velocity (in ft/s) for each time period. (i) [2,4] (ii) [3,4] (iii) [4,5] (iv) [4,6] (b) Plot the points in the table to create a graph of s as a function of t to estimate the instantaneous velocity (in ft/s) when t=3. (Round your answer to one decimal place.)
Transcript text: The table shows the position of a motorcyclist after accelerating from rest. $t$ (seconds) | 0 | 1 | 2 | 3 | 4 | 5 | 6 $s$ (feet) | 0 | 4.9 | 10.6 | 23.1 | 50.2 | 109.3 | 237.9 (a) Find the average velocity (in ft/s) for each time period. (i) $[2,4]$ (ii) $[3,4]$ (iii) $[4,5]$ (iv) $[4,6]$ (b) Plot the points in the table to create a graph of $s$ as a function of $t$ to estimate the instantaneous velocity (in ft/s) when $t=3$. (Round your answer to one decimal place.)
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Solution

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Solution Steps

Step 1: Calculate Average Velocity for [2,4]

The average velocity is given by the formula:

\[ v_{\text{avg}} = \frac{s(t_2) - s(t_1)}{t_2 - t_1} \]

For the interval \([2,4]\):

\[ v_{\text{avg}} = \frac{50.2 - 10.6}{4 - 2} = \frac{39.6}{2} = 19.8 \, \text{ft/s} \]

Step 2: Calculate Average Velocity for [3,4]

For the interval \([3,4]\):

\[ v_{\text{avg}} = \frac{50.2 - 23.1}{4 - 3} = \frac{27.1}{1} = 27.1 \, \text{ft/s} \]

Step 3: Calculate Average Velocity for [4,5]

For the interval \([4,5]\):

\[ v_{\text{avg}} = \frac{109.3 - 50.2}{5 - 4} = \frac{59.1}{1} = 59.1 \, \text{ft/s} \]

Final Answer

(i) \(19.8 \, \text{ft/s}\)

(ii) \(27.1 \, \text{ft/s}\)

(iii) \(59.1 \, \text{ft/s}\)

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