To determine the period of time during which the 4.0 N force acts on the object, we'll follow a detailed, step-by-step approach:
1. Identify the given values:
- Mass of the object ([tex]\( m \)[/tex]): 1.2 kg
- Initial velocity ([tex]\( v_i \)[/tex]): 2.0 m/s
- Final velocity ([tex]\( v_f \)[/tex]): 5.0 m/s
- Force ([tex]\( F \)[/tex]): 4.0 N
2. Calculate the change in velocity ([tex]\( \Delta v \)[/tex]):
[tex]\[
\Delta v = v_f - v_i
\][/tex]
Substituting the given values:
[tex]\[
\Delta v = 5.0 \, \text{m/s} - 2.0 \, \text{m/s} = 3.0 \, \text{m/s}
\][/tex]
3. Determine the acceleration ([tex]\( a \)[/tex]):
According to Newton's second law, the force acting on an object is equal to the mass of the object multiplied by its acceleration:
[tex]\[
F = m \cdot a
\][/tex]
Solving for acceleration:
[tex]\[
a = \frac{F}{m}
\][/tex]
Substituting the given values:
[tex]\[
a = \frac{4.0 \, \text{N}}{1.2 \, \text{kg}} = 3.33 \, \text{m/s}^2
\][/tex]
4. Calculate the time period ([tex]\( \Delta t \)[/tex]):
The formula for acceleration when dealing with constant acceleration is:
[tex]\[
a = \frac{\Delta v}{\Delta t}
\][/tex]
Solving for the time period:
[tex]\[
\Delta t = \frac{\Delta v}{a}
\][/tex]
Substituting the calculated values:
[tex]\[
\Delta t = \frac{3.0 \, \text{m/s}}{3.33 \, \text{m/s}^2} \approx 0.90 \, \text{s}
\][/tex]
Therefore, the period of time during which the force acts on the object is approximately 0.90 seconds. The correct answer is:
[tex]\[ \boxed{0.90 \, \text{s}} \][/tex]
So, the answer is [tex]\( \text{A} \)[/tex] 0.90 s.
