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Answer :
Final answer:
The work done by the brakes on a 500 kg car that decelerates from 54 km/hr and stops over a distance of 50 m has been calculated as -56.25 kJ. Since this exact figure is not available in the options provided by the student, there might be a discrepancy in the options or a need for rounding.
Explanation:
The student is asking about the work done by the brakes of a car weighing 500 kg that decelerates uniformly and stops. The car initially travels at a velocity of 54 km/hr and comes to a stop after travelling a distance of 50 m. To calculate the work done, we need to first convert the velocity to meters per second (m/s) since work is typically calculated using the metric system.
Velocity in m/s = (54 km/hr) × (1000 m/km) / (3600 s/hr) = 15 m/s.
Next, we use the work-energy principle which states that the work done is equal to the change in kinetic energy:
Work = Final Kinetic Energy - Initial Kinetic Energy = 0 - ½ × mass × (initial velocity)².
Therefore, Work = 0 - ½ × 500 kg × (15 m/s)² = -0.5 × 500 × 225 = -56250 Joules or -56.25 kJ.
The negative sign indicates that the work done by the brakes is in the opposite direction of the car's initial motion. Among the provided options, none exactly match the calculated work, but if it's a case of rounding or choices being approximate, the closest given option to the calculated work is -55 kJ (which is not listed in the provided options).
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