To find the final speed of the soccer player, we can use the kinematic equation that relates initial velocity, final velocity, acceleration, and displacement:
v^2 = u^2 + 2as
Where: v is the final velocity u is the initial velocity a is the acceleration s is the displacement
In this case: u = 1.8 m/s (initial velocity) a = 0.50 m/s^2 (acceleration) s = 10.0 m (displacement)
We can rearrange the equation to solve for v:
v^2 = u^2 + 2as v^2 = (1.8 m/s)^2 + 2 * (0.50 m/s^2) * (10.0 m) v^2 = 3.24 m^2/s^2 + 10 m^2/s^2 v^2 = 13.24 m^2/s^2
To find v, we take the square root of both sides:
v = √(13.24 m^2/s^2) v ≈ 3.64 m/s
Therefore, the final speed of the soccer player, after accelerating for a total distance of 10.0 meters, will be approximately 3.64 m/s.