To convey the magnitude of the train's acceleration to her crew, the engineer should calculate the acceleration clearly and provide relevant information. Here’s how to determine and explain it:
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Convert the final speed to meters per second:
- The peak speed of the train is given as 144 kilometers per hour.
- To convert this to meters per second: \[ 144 \text{ km/h} = \frac{144 \times 1000 \text{ m}}{3600 \text{ s}} = 40 \text{ m/s} \]
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Determine the time of acceleration:
- The time during which the acceleration occurs is 180 seconds.
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Calculate the acceleration:
- Since the train starts from a stationary position (initial speed \( v_0 = 0 \text{ m/s} \)) and reaches a final speed of \( v = 40 \text{ m/s} \), we can use the formula for acceleration \( a \): \[ a = \frac{v - v_0}{t} \]
- Substituting the values: \[ a = \frac{40 \text{ m/s} - 0 \text{ m/s}}{180 \text{ s}} = \frac{40 \text{ m/s}}{180 \text{ s}} \approx 0.222 \text{ m/s}^2 \]
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Information to communicate to the crew:
- The engineer should inform her crew that the train has an acceleration of approximately 0.22 m/s² over a duration of 180 seconds, starting from rest and reaching a peak speed of 40 m/s (144 km/h).
This information tells the crew not only the magnitude of the acceleration but also the context of the train's movement, which may be relevant for their operations and for maintaining passenger safety and comfort.
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