To determine the force required to stop the SUV, we will use the following physics principles:
1. Calculation of Acceleration:
- We know the initial speed ([tex]\( v_i \)[/tex]) of the SUV is [tex]\( 18 \, \text{m/s} \)[/tex].
- The final speed ([tex]\( v_f \)[/tex]) is [tex]\( 0 \, \text{m/s} \)[/tex] since the vehicle comes to a stop.
- The time ([tex]\( t \)[/tex]) over which the SUV is brought to a stop is [tex]\( 8 \)[/tex] seconds.
Using the formula for acceleration [tex]\( a \)[/tex]:
[tex]\[
a = \frac{v_f - v_i}{t}
\][/tex]
Substituting the known values:
[tex]\[
a = \frac{0 \, \text{m/s} - 18 \, \text{m/s}}{8 \, \text{seconds}}
\][/tex]
Simplifying this:
[tex]\[
a = \frac{-18 \, \text{m/s}}{8 \, \text{seconds}} = -2.25 \, \text{m/s}^2
\][/tex]
2. Application of Newton's Second Law:
- The mass ([tex]\( m \)[/tex]) of the SUV is [tex]\( 1550 \)[/tex] kg.
- Newton's second law states that the force ([tex]\( F \)[/tex]) is the product of mass and acceleration:
[tex]\[
F = m \times a
\][/tex]
Substituting the known values:
[tex]\[
F = 1550 \, \text{kg} \times (-2.25 \, \text{m/s}^2)
\][/tex]
Simplifying this:
[tex]\[
F = -3487.5 \, \text{N}
\][/tex]
Therefore, the required force to stop the SUV is [tex]\( -3487.5 \, \text{N} \)[/tex].
The best answer to the question is:
D. [tex]\(-3487.5 \, \text{N}\)[/tex]
