Calculating Acceleration of a Car using Power and Time

AI Thread Summary
To calculate the acceleration of a car with a mass of 880.0 kg and a net power output of 3700.0 W at a speed of 13.8 m/s, the correct approach involves using the differential form of power, P = Fv. By rearranging this equation, the force can be determined, and subsequently, acceleration can be calculated using Newton's second law. The initial calculations provided were incorrect due to the misuse of the power equation. After clarifying the method, the correct acceleration can be derived. The discussion emphasizes the importance of using the correct formulas in physics calculations.
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A car of mass 880.0 kg accelerates away from an intersection on a horizontal road. When the car speed is 13.8 m/s, the net power which the engine supplies is 3700.0 W ( in addition to the extra power required to make up for air resistance and friction). Calculate the acceleration of the car at the time.

I used the equation for power. P= change in work/ t
3700= (1/2)mv^2 / t
3700=83793.6 t
I solved for t to get 22.7 s.
I then used the equation for acceleration, change in v/ change in t
a= 13.8-0/ 22.7-0
and got the a to be .607 m/s^2
This wasn't right.

Can someone help me out? Thanks
 
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You have to use the differential form: P = \frac{dW}{dt} = F v. So the power is the force times the velocity, can you now find the acceleration?
 
Ok I got it.. thanks a lot!
 

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