To determine the magnitude of the retarding force acting on the box, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration:
Force = mass × acceleration
In this case, the mass of the box is given as 5 kg, and we need to find the acceleration. The change in velocity (∆v) can be calculated by subtracting the final velocity (4 m/s) from the initial velocity (8 m/s):
∆v = 4 m/s - 8 m/s = -4 m/s
The negative sign indicates that the velocity is decreasing.
Acceleration (a) can be calculated using the formula:
Acceleration = ∆v / ∆t
where ∆t is the time interval. In this case, ∆t is given as 1.5 seconds:
Acceleration = -4 m/s / 1.5 s = -2.67 m/s²
The negative sign indicates that the acceleration is in the opposite direction to the initial velocity.
Now that we have the mass (m = 5 kg) and acceleration (a = -2.67 m/s²), we can calculate the force:
Force = mass × acceleration Force = 5 kg × (-2.67 m/s²) Force = -13.35 N
The magnitude of the force is 13.35 Newtons. Note that the negative sign indicates that the force is acting in the opposite direction to the motion of the box.