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Answer :
Final answer:
The average power developed by the engine of a car accelerating uniformly and undergoing constant air resistance can be calculated by determining the net force, work done, and then calculating power as work done divided by time. The car's engine develops an average power of approximately 2654 watts under the given circumstances.
Explanation:
The main answer to this question is obtained through a few physics calculations. The car is accelerating from the rest to its final speed, hence we'll first find out the force exerted by the car's engine, using the formula Force = mass x acceleration. Given the mass of the car is 1.50x10³ kg and acceleration (final speed/time) is (18.6m/s)/(11.4s) = 1.63 m/s². So, the force by the engine would be 1.50x10³ kg x 1.63 m/s² = 2445 N.
However, there is a constant resistance force of 400 N opposing the car's motion. So, the net force needed by the car would be 2445 N + 400 N = 2845 N. Now, we calculate the work done using the formula Work = Force x distance. The distance covered can be calculated using the formula distance = 0.5 x acceleration x (time)² = 0.5 x 1.63 m/s² x (11.4s)² = 10.64 m. Hence, work done = 2845 N x 10.64 m = 30257.6 J.
Now, the average power developed by the engine is work done/time = 30257.6 J/11.4s = 2653.8 W. Therefore, the car's engine develops an average power of approximately 2654 watts during this period.
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