Question
If a boat slows from 55 m/s to 45 m/s in a period of 5.0 s, what was the average acceleration?
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Answered by
GPT-4o mini
To calculate the average acceleration, we can use the formula:
\[
a = \frac{v_f - v_i}{t}
\]
where:
- \( a \) is the average acceleration,
- \( v_f \) is the final velocity,
- \( v_i \) is the initial velocity,
- \( t \) is the time period over which the change occurs.
Given:
- \( v_f = 45 \) m/s (final velocity),
- \( v_i = 55 \) m/s (initial velocity),
- \( t = 5.0 \) s (time).
Now, we can substitute these values into the equation:
\[
a = \frac{45 \, \text{m/s} - 55 \, \text{m/s}}{5.0 \, \text{s}} = \frac{-10 \, \text{m/s}}{5.0 \, \text{s}} = -2 \, \text{m/s}^2
\]
The average acceleration of the boat is \(-2 \, \text{m/s}^2\). This negative sign indicates that the boat is decelerating.
\[
a = \frac{v_f - v_i}{t}
\]
where:
- \( a \) is the average acceleration,
- \( v_f \) is the final velocity,
- \( v_i \) is the initial velocity,
- \( t \) is the time period over which the change occurs.
Given:
- \( v_f = 45 \) m/s (final velocity),
- \( v_i = 55 \) m/s (initial velocity),
- \( t = 5.0 \) s (time).
Now, we can substitute these values into the equation:
\[
a = \frac{45 \, \text{m/s} - 55 \, \text{m/s}}{5.0 \, \text{s}} = \frac{-10 \, \text{m/s}}{5.0 \, \text{s}} = -2 \, \text{m/s}^2
\]
The average acceleration of the boat is \(-2 \, \text{m/s}^2\). This negative sign indicates that the boat is decelerating.
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