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Answer :
To determine the average power output of the dragster, we calculate the work done against friction and to accelerate the car, which totals 3,163,750 Joules. Over the time of 7.54 seconds, the average power is approximately 419,665 watts or 419.665 kilowatts.
To calculate the average power output of the dragster, we must first determine the work done by the dragster, which includes both the work to overcome the frictional force and the work done to accelerate the car to its final speed. The work done against friction is the product of the frictional force and the distance (Work = Frictional force x distance). The work to accelerate the car can be found using the kinetic energy formula (Work = rac{1}{2}mv^2).
Given:
- Mass (m) = 450 kg
- Final speed (v) = 109 m/s
- Distance (d) = 400 m
- Frictional force (f) = 1,198 N
- Time (t) = 7.54 s
Calculating the work done against friction: Workfriction = f x d = 1,198 N x 400 m = 479,200 J (Joules).
Calculating the kinetic energy: Workkinetic = rac{1}{2}mv^2 = rac{1}{2} x 450 kg x (109 m/s)^2 = 2,684,550 J.
Total work done by the dragster: Total work = Workfriction + Workkinetic = 479,200 J + 2,684,550 J = 3,163,750 J.
The average power output is the total work done divided by the time: Power = Total work / t = 3,163,750 J / 7.54 s = approximately 419,665 watts.
To convert watts to kilowatts, divide by 1,000: Power (kW) = 419,665 watts / 1,000 = 419.665 kW.
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