Find the power of a boat that accelerated

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In summary, a 3.5x107 kg ship traveling at 7 m/s is accelerated forward with a force of 4.5x105 N over a distance of 2 km. The final speed is 10 m/s and it takes 233.33 seconds for the ship to traverse the distance. The average power produced by the engines is 3.9 x 106 watts, calculated using the formula P = W/t = Fvavg. There was a confusion regarding the formula for average velocity, but it was resolved with the correct formula of (vf + vi)/2.
  • #1
jehan4141
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A 3.5x107 kg ship is traveling at 7 m/s. The ship is accelerated forward with a F of 4.5 x 105 N over a distance of 2 km.

What is the final speed? Vf = 10 m/s

How long does it take the ship to traverse the 2 km? T = 233.33 seconds

What is the average power which the engines had to produce to accelerate the ship in part 1? I need help on this please.

You can do P = W/t = (4.5x105 x 2000) / 233.333

P = 3.9 x 106 watts which is the right answer.

However, how come you can't do P = (F)(avg velocity)

P = 4.5x105 * (3/2) = 675000 watts??
 
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  • #2
Hi,

Where'd you get your avg velocity from?

You can use this formula, and in fact the two methods are equivalent, since:

P = W/t = Fd/t = F(d/t) = Fvavg

vavg = d/t = 2000 m / 233.33 s = 8.57 m/s

4.5e5 N * 8.57 m/s = 3.9e6 Nm/s (= J/s = W)
 
  • #3
Ah I see. It looks like you were confused in your formula for avg. velocity. It's (vf + vi)/2 NOT (vf - vi)/2.

(10 m/s + 7 m/s)/2 = 17/2 m/s = 8.5 m/s
 
  • #4
cepheid said:
Ah I see. It looks like you were confused in your formula for avg. velocity. It's (vf + vi)/2 NOT (vf - vi)/2.

(10 m/s + 7 m/s)/2 = 17/2 m/s = 8.5 m/s


Oh my goodness! Your eyes are so good! I have been using energy formulas all day that do Xf-Xi all day! Such a silly mistake thank you so much! it is so late and my brain if frazzled :)
 
  • #5



I would like to clarify that power is defined as the rate at which work is done or energy is transferred. In this scenario, the average power produced by the engines is equivalent to the average rate at which the ship's kinetic energy was increased. Therefore, the correct approach to calculating the average power would be to use the formula P = W/t, where W is the work done and t is the time taken. This is because the engines are constantly exerting a force to accelerate the ship over a distance, resulting in work being done.

The formula P = F * v is used for calculating instantaneous power, where F is the force applied and v is the velocity at that instant. In this case, the force and velocity are not constant throughout the entire acceleration process, so using this formula would not give an accurate representation of the average power.

Therefore, the correct approach to calculating the average power would be to use the formula P = W/t, as mentioned before. This would give a more accurate representation of the average power produced by the engines during the acceleration process.
 

What is the formula for finding the power of a boat that accelerated?

The formula for finding the power of a boat that accelerated is P = m x a x v, where P represents power, m represents mass, a represents acceleration, and v represents velocity.

How do you calculate the mass of a boat?

The mass of a boat can be calculated by adding the weight of the boat and all of its contents, including passengers, cargo, and fuel.

What is the difference between acceleration and velocity?

Acceleration is the rate of change of an object's velocity over time, while velocity is the speed and direction of an object's motion.

Why is it important to find the power of a boat that accelerated?

Knowing the power of a boat that accelerated is important for understanding its performance and capabilities. It can also help in determining the appropriate engine size and fuel efficiency.

How does the power of a boat that accelerated affect its speed?

The power of a boat that accelerated is directly proportional to its speed. As the power increases, the boat will be able to accelerate faster and reach higher speeds.

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