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Answer :
To solve the problem, we need to determine the force required to accelerate the snowmobile from its initial velocity to a specified final velocity.
1. Understand the Given Information:
- Initial velocity ([tex]\(v\)[/tex]) = 10 meters/second
- Final velocity ([tex]\(b\)[/tex]) = 18 meters/second (this is assumed based on context)
- Total mass ([tex]\(m\)[/tex]) = 280 kilograms
2. Use the Formula for Acceleration ([tex]\(a\)[/tex]):
Acceleration is calculated using the formula:
[tex]\[
a = \frac{\text{final velocity} - \text{initial velocity}}{t}
\][/tex]
We assume that the time period ([tex]\(t\)[/tex]) is 5 seconds. This can be any reasonable duration over which the snowmobile accelerates.
3. Calculate Acceleration:
Substitute the given values into the acceleration formula:
[tex]\[
a = \frac{18 - 10}{5} = \frac{8}{5} = 1.6 \text{ meters/second}^2
\][/tex]
4. Apply the Force Formula ([tex]\(F = ma\)[/tex]):
Using the mass of the snowmobile and Sully, calculate the force:
[tex]\[
F = 280 \times 1.6 = 448 \text{ Newtons}
\][/tex]
With the calculations complete, the force required to accelerate the snowmobile is 448 Newtons. This does not match any of the choices provided, suggesting an error in the options or assumptions made regarding time. However, the calculated force is 448 N based on the available information.
1. Understand the Given Information:
- Initial velocity ([tex]\(v\)[/tex]) = 10 meters/second
- Final velocity ([tex]\(b\)[/tex]) = 18 meters/second (this is assumed based on context)
- Total mass ([tex]\(m\)[/tex]) = 280 kilograms
2. Use the Formula for Acceleration ([tex]\(a\)[/tex]):
Acceleration is calculated using the formula:
[tex]\[
a = \frac{\text{final velocity} - \text{initial velocity}}{t}
\][/tex]
We assume that the time period ([tex]\(t\)[/tex]) is 5 seconds. This can be any reasonable duration over which the snowmobile accelerates.
3. Calculate Acceleration:
Substitute the given values into the acceleration formula:
[tex]\[
a = \frac{18 - 10}{5} = \frac{8}{5} = 1.6 \text{ meters/second}^2
\][/tex]
4. Apply the Force Formula ([tex]\(F = ma\)[/tex]):
Using the mass of the snowmobile and Sully, calculate the force:
[tex]\[
F = 280 \times 1.6 = 448 \text{ Newtons}
\][/tex]
With the calculations complete, the force required to accelerate the snowmobile is 448 Newtons. This does not match any of the choices provided, suggesting an error in the options or assumptions made regarding time. However, the calculated force is 448 N based on the available information.
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