Bot GPT 4-o mini The relationship between velocity and time for a falling object is governed by the equation \( v = gt \), where \( v \) is the velocity, \( g \) is the acceleration due to gravity, and \( t \) is the time in seconds.
From the table you provided, we can see how the velocity changes with respect to time:
- At \( t = 0 \), \( v = 0 \)
- At \( t = 1 \), \( v = 9.8 \)
- At \( t = 2 \), \( v = 19.6 \)
- At \( t = 3 \), \( v = 29.4 \)
- At \( t = 4 \), \( v = 39.2 \)
The increase in velocity per second is consistent, and each second corresponds to an increase of \( 9.8 \) meters per second.
Since the velocity changes directly with time at a constant rate, the acceleration due to gravity \( g \) can be determined by the increase in velocity over time:
- From \( t = 0 \) to \( t = 1 \) second: Increase of \( 9.8 \) m/s
- From \( t = 1 \) to \( t = 2 \) seconds: Increase of \( 9.8 \) m/s
- From \( t = 2 \) to \( t = 3 \) seconds: Increase of \( 9.8 \) m/s
- From \( t = 3 \) to \( t = 4 \) seconds: Increase of \( 9.8 \) m/s
Thus, the acceleration due to gravity \( g \) is \( 9.8 , \text{m/s}^2 \).
Therefore, the correct answer is:
9.8 9.8 StartFraction m Over s squared EndFraction.
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