To determine the force required to stop the SUV, we need to follow these steps:
1. Identify the given values:
- Initial speed ([tex]\(v_i\)[/tex]) of the SUV: [tex]\(18 \, \text{m/s}\)[/tex]
- Mass ([tex]\(m\)[/tex]) of the SUV: [tex]\(1,550 \, \text{kg}\)[/tex]
- Time ([tex]\(t\)[/tex]) in which the SUV should stop: [tex]\(8 \, \text{seconds}\)[/tex]
2. Determine the final speed ([tex]\(v_f\)[/tex]):
Since the SUV is coming to a stop, the final speed is [tex]\(0 \, \text{m/s}\)[/tex].
3. Calculate the acceleration ([tex]\(a\)[/tex]):
Using the formula for acceleration:
[tex]\[
a = \frac{v_f - v_i}{t}
\][/tex]
Substituting the known values:
[tex]\[
a = \frac{0 \, \text{m/s} - 18 \, \text{m/s}}{8 \, \text{seconds}} = \frac{-18 \, \text{m/s}}{8 \, \text{seconds}} = -2.25 \, \text{m/s}^2
\][/tex]
4. Calculate the force ([tex]\(F\)[/tex]):
Using Newton's second law of motion ([tex]\(F = ma\)[/tex]):
[tex]\[
F = 1,550 \, \text{kg} \times -2.25 \, \text{m/s}^2 = -3,487.5 \, \text{N}
\][/tex]
Thus, the force that must be applied to stop the SUV in 8 seconds is [tex]\( -3,487.5 \, \text{N} \)[/tex]. The correct answer is:
D. [tex]\(-3,487.5 \, \text{N}\)[/tex]
