To determine the force required to stop an SUV traveling at a speed of 18 meters per second over a duration of 8 seconds, we need to follow these steps:
### Step 1: Determine the acceleration
We start by calculating the acceleration using the following formula:
[tex]\[ a = \frac{{v_f - v_i}}{t} \][/tex]
Where:
- [tex]\( v_f \)[/tex] is the final velocity (0 m/s, since the SUV stops),
- [tex]\( v_i \)[/tex] is the initial velocity (18 m/s), and
- [tex]\( t \)[/tex] is the time (8 seconds).
So, plugging in the values:
[tex]\[ a = \frac{0 - 18}{8} \][/tex]
[tex]\[ a = \frac{-18}{8} \][/tex]
[tex]\[ a = -2.25 \, \text{m/s}^2 \][/tex]
### Step 2: Calculate the force
Next, we use Newton's second law to find the force. The formula is:
[tex]\[ F = m \cdot a \][/tex]
Where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass (1,550 kg), and
- [tex]\( a \)[/tex] is the acceleration we just calculated (-2.25 m/s²).
Substituting in the values:
[tex]\[ F = 1550 \cdot (-2.25) \][/tex]
[tex]\[ F = -3487.5 \, \text{N} \][/tex]
### Step 3: Select the correct answer
The force required to stop the SUV in 8 seconds is [tex]\(-3487.5 \, \text{N}\)[/tex], which corresponds to option A.
Thus, the correct answer is:
A. [tex]\(-3487.5 \, \text{N}\)[/tex]
