A force of $50N$ is required to push a car on a level road with constant velocity of $10m/s$. The mass of the car is $500kg$. What force should be applied to make the car accelerate at $1m/s^2$?
I though that $F=ma=(500)(1)=500N$. But the answer happens to be 550N, also I don't know why the constant velocity was provided.
The $50 \text{ N}$ extra is what is being used to overcome whatever losses (friction, air resistance, etc.) to keep the car at a constant velocity. Its stated in the first sentence of your problem. You have:
$F_{tot} = F_{app} - F_{loss}$
Initially, $F_{tot} = 0$, and $F_{app} = \text{50 N}$, so $F_{loss} = \text{50 N}$. Assuming the increase in acceleration doesn't introduce any new loss, you are correct that you need to apply $\text{500 N}$ of force, for the total force. To overcome the losses, you need $\text{50 N}$ of additional force. Hence, the force applied is $\text{550 N}$
