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Answer :
To determine the acceleration of Runner A and Runner B during the final 10 seconds of the race, we can use the following formula:
Acceleration (a) = (Final Velocity - Initial Velocity) / Time
Given:
- Initial velocity for both runners: +14 km/h
- Final velocity for Runner A: +20 km/h
- Final velocity for Runner B: +18 km/h
- Time: 10 seconds
Let's calculate the accelerations for Runner A and Runner B:
For Runner A:
Acceleration (Runner A) = (+20 km/h - +14 km/h) / 10 seconds
Converting the velocities to m/s and the time to seconds:
Acceleration (Runner A) = ((20 km/h - 14 km/h) * (1000 m/km) / (3600 s/h)) / 10 seconds
Simplifying the calculation:
Acceleration (Runner A) = (6 km/h * (1000 m/km) / (3600 s/h)) / 10 seconds
Acceleration (Runner A) = (6000 m / 36000 s) / 10 seconds
Acceleration (Runner A) = 0.1667 m/s²
For Runner B:
Acceleration (Runner B) = (+18 km/h - +14 km/h) / 10 seconds
Converting the velocities to m/s and the time to seconds:
Acceleration (Runner B) = ((18 km/h - 14 km/h) * (1000 m/km) / (3600 s/h)) / 10 second
Simplifying the calculation:
Acceleration (Runner B) = (4 km/h * (1000 m/km) / (3600 s/h)) / 10 seconds
Acceleration (Runner B) = (4000 m / 36000 s) / 10 seconds
Acceleration (Runner B) = 0.1111 m/s²
Therefore, the accelerations of Runner A and Runner B during the final 10 seconds of the race are:
- Runner A: 0.1667 m/s²
- Runner B: 0.1111 m/s²
None of the provided options match these values.
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