To find the net force acting on the body, we need to follow a step-by-step approach that involves a couple of physics principles, specifically Newton's second law of motion and the kinematic equations.
1. Determine the acceleration:
We start by finding the acceleration of the body. According to the kinematic equation:
[tex]\[
\text{acceleration} = \frac{\text{final velocity} - \text{initial velocity}}{\text{time}}
\][/tex]
Given that the body starts from rest, the initial velocity is [tex]\(0 \, m/s\)[/tex]. The final velocity is [tex]\(5.8 \, m/s\)[/tex], and the time taken is [tex]\(3.9 \, s\)[/tex].
Substituting the values into the equation:
[tex]\[
\text{acceleration} = \frac{5.8 \, m/s - 0 \, m/s}{3.9 \, s} = \frac{5.8}{3.9} \approx 1.487 \, m/s^2
\][/tex]
2. Calculate the net force:
Using Newton's second law, which states that force equals mass times acceleration ([tex]\(F = ma\)[/tex]), we can calculate the net force acting on the body.
Given:
- Mass of the body, [tex]\(m = 4 \, kg\)[/tex]
- Acceleration, [tex]\(a \approx 1.487 \, m/s^2\)[/tex]
Substituting these values into the formula:
[tex]\[
F = m \cdot a = 4 \, kg \cdot 1.487 \, m/s^2 \approx 5.949 \, N
\][/tex]
When rounded to one decimal place, the net force is:
[tex]\[
F \approx 5.9 \, N
\][/tex]
So, the net force acting on the body is [tex]\(5.9 \, N\)[/tex]. Therefore, the correct answer is:
5.9 N
