Find Average Power Given Mass and Velocity

In summary, The conversation discusses how to calculate the average power produced by an engine based on the change in kinetic energy of a vehicle. The initial and final velocities, along with the time, are given to calculate the acceleration, force, and displacement of the body. One person had trouble solving the problem due to using the incorrect final velocity.
  • #1
Snape1830
65
0
During 12 s an engine increases the speed of a 1.5×103-kg vehicle from 13 m/s to 27 m/s. Assuming no losses, what average power is the engine producing?

P = W/t
W=FΔx
W=ΔKE
ΔKE=mvf2-mfi2

I tried finding the change in kinetic energy to solve the problem, but it didn't work. I got 3.4E3 W. I'm really lost. I've never done a power problem given only velocity and mass.
 
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  • #2
You aren't just given velocity and mass. You are given the initial and final velocities, along with the time. From this you can easily calculate the acceleration of the body.

Now that you have acceleration, you also get the force. And displacement should be easy to calculate from the equations of motion. Should be pretty easy from here on...
 
  • #3
Infinitum said:
You aren't just given velocity and mass. You are given the initial and final velocities, along with the time. From this you can easily calculate the acceleration of the body.

Now that you have acceleration, you also get the force. And displacement should be easy to calculate from the equations of motion. Should be pretty easy from here on...

Thanks! And I realized my problem was that for some strange reason I was using 14 m/s as the final velocity instead of 27 m/s.
 
  • #4
Glad to be of help! :smile:
 
  • #5


I would first clarify what type of power is being referred to in this scenario - is it the power output of the engine or the power required to move the vehicle? Assuming it is the power output of the engine, we can use the formula P = Fv, where F is the force applied and v is the velocity.

To find the force, we can use Newton's second law, F = ma, where m is the mass of the vehicle and a is the acceleration. In this case, the acceleration can be calculated as (27 m/s - 13 m/s)/12 s = 1 m/s^2. Therefore, the force applied by the engine is (1.5x10^3 kg)(1 m/s^2) = 1.5x10^3 N.

Now, we can plug in the values in the formula for power: P = (1.5x10^3 N)(27 m/s) = 4.05x10^4 W. This is the average power produced by the engine during the 12 seconds it took to increase the speed of the vehicle from 13 m/s to 27 m/s.

It is important to note that this is the theoretical power output of the engine, assuming no losses. In reality, there will always be some losses (such as friction) that will decrease the actual power output of the engine.
 

1. What is the formula for finding average power given mass and velocity?

The formula for finding average power given mass and velocity is P = m * v, where P is power, m is mass, and v is velocity. This is also known as the work-energy theorem, where power is equal to the change in energy over time.

2. How do mass and velocity affect average power?

Mass and velocity both have a direct effect on average power. The greater the mass, the more energy is required to move it at a certain velocity. Similarly, the higher the velocity, the more energy is needed to maintain that speed. Therefore, the greater the mass and velocity, the higher the average power will be.

3. Can average power be negative?

Yes, average power can be negative. This means that the object is losing energy over time instead of gaining it. This could happen if the object is slowing down or moving against a force, resulting in a negative change in energy.

4. What units are used to measure average power?

The standard unit for power is watts (W), which is equal to one joule per second. However, other units such as horsepower (hp) and British thermal units per hour (BTU/h) can also be used to measure average power.

5. How is average power calculated in real-life situations?

In real-life situations, average power is often calculated using more complex formulas that take into account other factors such as friction, air resistance, and efficiency. In addition, instruments such as power meters and dynamometers are used to measure average power in various systems, such as engines, turbines, and motors.

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