Calculating Acceleration of a Car using Power and Time

[Punchlinegirl]

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

 

[Physics Monkey]

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?

 

[Punchlinegirl]

Ok I got it.. thanks a lot!