Answer
$P = 2.9\times 10^4~W$
$P = 38~hp$
Work Step by Step
We can use the change in velocity to find the average acceleration:
$a = \frac{\Delta v}{\Delta t} = \frac{(-30~km/h)(1000~m/km)(1~h/3600~s)}{7.0s} = -1.19~m/s^2$
Then, we use the magnitude of acceleration to find the average force opposing the car's motion:
$F = ma = (1080~kg)(1.19~m/s^2) = 1285~N$
Next, we use the average force to find the power when the car is moving at a speed of 80 km/h:
$P = F\cdot v$
$P = (1285~N)(80~km/h)(1000~m/km)(1~h/3600~s)$
$P = 2.9\times 10^4~W$
Since we want the car to travel at a constant speed, the car needs to provide the same magnitude of power:
$P = 2.9\times 10^4~W$
$P = (2.9\times 10^4~W)(\frac{1~hp}{746~W}) = 38~hp$
