Final answer:
The average power needed for the speedboat to go from rest to 20.0 m/s in 5.0 s is 1,600 kW.
Step-by-step explanation:
To find the average power, we can use the formula:
Power = Work / Time
First, let's find the work done. The work done is equal to the change in kinetic energy. The initial kinetic energy is zero since the speedboat is at rest. The final kinetic energy can be found using the formula:
Kinetic Energy = 1/2 * mass * velocity^2
Substituting the given values, we have:
Final Kinetic Energy = 1/2 * 2,000 kg * (20.0 m/s)^2
Now, find the change in kinetic energy:
Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy
Since the initial kinetic energy is zero, the change in kinetic energy is equal to the final kinetic energy.
Next, calculate the time:
Time = 5.0 s
Finally, substitute the values into the power formula:
Power = Change in Kinetic Energy / Time
Calculating this gives:
Power = Final Kinetic Energy / Time
Power = (1/2 * 2,000 kg * (20.0 m/s)^2) / 5.0 s
Simplifying this gives a power of 1,600 kW.