To determine the final velocity of the brick, we need to consider the initial velocity, the distance traveled, and any relevant accelerations or decelerations.
However, without information about any external forces acting on the brick, we can assume that the only force acting on the brick is gravity. Therefore, we can assume that the brick is undergoing free fall, and the acceleration due to gravity is approximately 9.8 m/s², directed downward.
Using the equation of motion for uniformly accelerated linear motion:
v^2 = u^2 + 2as
Where: v = final velocity u = initial velocity a = acceleration s = distance
In this case, the initial velocity (u) is given as 6 m/s, the acceleration (a) is the acceleration due to gravity (-9.8 m/s²), and the distance traveled (s) is 40 m.
Plugging in these values into the equation, we have:
v^2 = (6 m/s)^2 + 2 * (-9.8 m/s²) * (40 m)
Simplifying the equation:
v^2 = 36 m²/s² + (-784 m²/s²)
v^2 = -748 m²/s²
Since we have a negative value for v^2, it indicates that the final velocity will be directed upward. However, in this case, since the brick is initially given a downward velocity, we can infer that it will eventually come to a stop and start moving upward due to the deceleration caused by gravity.
To find the magnitude of the final velocity, we take the square root of the absolute value of v^2:
v = √(748 m²/s²) ≈ 27.3 m/s
Therefore, the final velocity of the brick, after traveling a distance of 40 m, would be approximately 27.3 m/s, directed upward.