Find Average Power Given Mass and Velocity

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SUMMARY

The discussion centers on calculating the average power produced by an engine that accelerates a 1.5×103-kg vehicle from an initial velocity of 13 m/s to a final velocity of 27 m/s over a time period of 12 seconds. The correct approach involves using the formula P = W/t, where W is the work done, calculated as the change in kinetic energy (ΔKE = mvf2 - mvi2). A common mistake noted was using the incorrect final velocity, which led to an erroneous power calculation of 3.4E3 W.

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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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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...
 
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.
 
Glad to be of help! :smile:
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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