Sure, let's solve this step by step.
1. Given data:
- Mass of the object, [tex]\( m = 1.5 \)[/tex] kg
- Initial velocity, [tex]\( v_i = +15 \)[/tex] m/s
- Final velocity, [tex]\( v_f = +22 \)[/tex] m/s
- Time interval, [tex]\( t = 3.5 \)[/tex] seconds
2. Calculate the change in velocity ([tex]\(\Delta v\)[/tex]):
[tex]\[ \Delta v = v_f - v_i \][/tex]
[tex]\[ \Delta v = 22 \, \text{m/s} - 15 \, \text{m/s} \][/tex]
[tex]\[ \Delta v = 7 \, \text{m/s} \][/tex]
3. Calculate the impulse delivered to the object:
Impulse ([tex]\( J \)[/tex]) is given by:
[tex]\[ J = m \cdot \Delta v \][/tex]
Plugging in the values,
[tex]\[ J = 1.5 \, \text{kg} \times 7 \, \text{m/s} \][/tex]
[tex]\[ J = 10.5 \, \text{N} \cdot \text{s} \][/tex]
Thus, the impulse delivered to the object is [tex]\( 10.5 \, \text{N} \cdot \text{s} \)[/tex].
Considering the given multiple-choice options:
- [tex]\( 3.0 \, \text{N} \cdot \text{s} \)[/tex]
- [tex]\( 11 \, \text{N} \cdot \text{s} \)[/tex]
- [tex]\( 25 \, \text{N} \cdot \text{s} \)[/tex]
- [tex]\( 56 \, \text{N} \cdot \text{s} \)[/tex]
The closest option to our calculated value [tex]\( 10.5 \, \text{N} \cdot \text{s} \)[/tex] is [tex]\( 11 \, \text{N} \cdot \text{s} \)[/tex].
So, the correct answer is [tex]\( 11 \, \text{N} \cdot \text{s} \)[/tex].
