Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
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]
### 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]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.