To find the acceleration of the runner, you can use the formula for acceleration:
\[ a = \frac{\Delta v}{\Delta t} \]
where:
- \( \Delta v \) is the change in velocity,
- \( \Delta t \) is the time over which the change occurs.
However, in this problem, we are not given the time (\(\Delta t\)). Instead, we can find the change in velocity (\(\Delta v\)):
\[ \Delta v = v_f - v_i \]
where:
- \( v_f = 4.17 , \text{m/s} \) (final velocity),
- \( v_i = 3.95 , \text{m/s} \) (initial velocity).
Calculating the change in velocity:
\[ \Delta v = 4.17 , \text{m/s} - 3.95 , \text{m/s} = 0.22 , \text{m/s} \]
Now, without any information about the time over which this change occurs, we cannot compute the acceleration in \( \text{m/s}^2 \) without further details. If we assume the change in velocity happens over some very small duration, we can't definitively state an acceleration value with a lack of time.
But since the only provided options in the responses indicate the specific changes in speed, we see an increase of \(0.22\) m/s. This implies that if we assume the time interval is \(1\) second (for example), the acceleration would be \(0.22 , \text{m/s}^2\).
Therefore, of the provided options, if you assume the time interval is implicitly defined (possibly as \(1\) second), the best conclusion we can draw from the change in velocity is:
0.22 m/s².
However, please keep in mind, without \(\Delta t\), this is purely a conceptual result.
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