Final answer:
The final velocity of the mass after 3.0 seconds is 18 m/s west. Using Newton's second law and kinematic equations, the final velocity of the mass is calculated to be 18 m/s westward. This velocity is reached after an 8.0 N westward force is applied for 3.0 seconds. The options given in the question do not match this correct answer. The correct answer is B.
Step-by-step explanation:
To find the final velocity of the object, we can use the equation:
Vf = Vi + (F/m)t
Where Vf is the final velocity, Vi is the initial velocity, F is the force, m is the mass, and t is the time interval.
In this case, the initial velocity is 12 m/s west, the force is 8 N west, the mass is 4 kg, and the time interval is 3 seconds.
Plugging in these values, we get:
Vf = 12 m/s + (8 N / 4 kg)(3 s)
Vf = 12 m/s + 6 m/s
Vf = 18 m/s west
Therefore, the final velocity of the mass after 3.0 seconds is 18 m/s west.
Using Newton's second law and kinematic equations, the final velocity of the mass is calculated to be 18 m/s westward. This velocity is reached after an 8.0 N westward force is applied for 3.0 seconds. The options given in the question do not match this correct answer.
To determine the final velocity of a mass after a certain time interval, we need to apply the principles of kinematics. In this scenario, a 4.0 kg mass experiences a constant westward force of 8.0 N for 3.0 seconds. The initial velocity is given as 12 m/s to the west. We can use Newton's second law (F = ma) to find the acceleration and then use the kinematic equation (vf = vi + at) to find the final velocity (vf).
First, calculate the acceleration (a) using the formula: a = F/m. Here, F = 8.0 N and m = 4.0 kg, so a = 8.0 N / 4.0 kg = 2.0 m/s² westward.
Now, use the kinematic equation to calculate the final velocity vf = vi + at, where vi = 12 m/s west, a = 2.0 m/s² west, and t = 3.0 s:
vf = 12 m/s + (2.0 m/s² × 3.0 s)
vf = 12 m/s + 6 m/s
vf = 18 m/s to the west
However, the question provides options that do not include 18 m/s west. The provided options might be incorrect or there might be a typo in the question. The correct calculation shows that the final velocity is 18 m/s west, not any of the options given (4 m/s west, 8 m/s west, 12 m/s west, or 16 m/s west).