A car sitting at a red light begins to accelerate at $2\mathrm{.}0$ m$/$s$\mathrm{²}$ when the light turns green. It continues with this acceleration until it reaches a speed of $20$ m$/$s$.$ It then travels at this speed for another few minutes. How far does the car travel in the first $50$ s after the light changes to green? 

Express your answer in meters.