Power needed to maintain speed against resistance in a coasting car

[melito]

A car with a mass of 1072 kg is coasting in neutral on a straight,level road. It slows down, and its speed as a function of time is given by the equation:
v(t) = a − bt + ct2



Constant Value Units
a 26.8 m/s
b 0.310 m/s2
c 2.10·10^-3 m/s2

At a time of 38.0 s the speed, as given by the above equation, is 18.05 m/s. Calculate the power which the engine must deliver (to compensate for air resistance and rolling resistance) in order to maintain that speed.

This is the problem; but I couldn't solve it. Please help.

 

[PhanthomJay]

Have you made an attempt at a solution (per Forum rules)? Try using Newton's second law to find the force acting on the car after 38 seconds, then recognize that the car moves at constant velocity thereafter , and use the equation for power required to maintain that speed. Please list the relevant equations. And welcome to PF!