If a 0.50-kg block initially at rest on a frictionless, horizontal surface is acted upon by a force of 8.0 N for a distance of 4 m, then what would be the block's velocity?
To find the block's velocity, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. Since the block is initially at rest, we can assume it starts from rest and has zero initial velocity. Additionally, since the surface is frictionless, there are no opposing forces to consider.
The force acting on the block is given as 8.0 N and the mass is given as 0.50 kg. We can calculate the acceleration using Newton's second law:
Force = mass x acceleration
8.0 N = 0.50 kg x acceleration
Rearranging the equation to solve for acceleration:
acceleration = Force / mass
acceleration = 8.0 N / 0.50 kg
acceleration = 16 m/s^2
Now that we have the acceleration, we can use the equations of motion to find the final velocity of the block. We can use the following equation:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity (which is 0 m/s since the block starts from rest)
a = acceleration (which is 16 m/s^2 as calculated above)
s = distance (which is given as 4 m)
Plugging in the values into the equation:
v^2 = 0 + 2 x 16 m/s^2 x 4 m
v^2 = 128 m^2/s^2
Taking the square root of both sides:
v = √(128 m^2/s^2)
v ≈ 11.31 m/s
Therefore, the block's velocity after being acted upon by a force of 8.0 N for a distance of 4 m would be approximately 11.31 m/s.
a = F/M = 8/0.5 = 16 m/s^2
V^2 = Vo + 2a*d
Vo = 0
a = 16 m/s^2
d = 4 m.
Solve for V(m/s).