To find the final velocity of the car, we can use the following equation of motion:
v^2 = u^2 + 2as
where: v is the final velocity, u is the initial velocity (0 m/s in this case), a is the acceleration (0.5 m/s^2 in this case), and s is the displacement (800 m in this case).
Plugging in the given values into the equation, we get:
v^2 = 0^2 + 2 * 0.5 * 800
Simplifying further:
v^2 = 0 + 800
v^2 = 800
Taking the square root of both sides, we find:
v ≈ 28.28 m/s
Therefore, the final velocity of the car, after accelerating at a constant rate of 0.5 m/s^2 for a distance of 800 m, is approximately 28.28 m/s.