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Answer :
To solve the problem, let's follow these steps:
1. Understand the given data:
- Total mass with Sully on the snowmobile is 280 kilograms.
- Final velocity [tex]\( v \)[/tex] is 8 meters per second.
- Initial velocity [tex]\( \psi \)[/tex] is assumed to be 0 meters per second, meaning the snowmobile started from rest.
- Time [tex]\( t \)[/tex] taken to accelerate to the final velocity is 14 seconds.
2. Calculate the acceleration:
The formula for acceleration [tex]\( a \)[/tex] is:
[tex]\[
a = \frac{v - \psi}{t}
\][/tex]
Substituting the given values:
[tex]\[
a = \frac{8 - 0}{14} = \frac{8}{14} \approx 0.5714 \, \text{m/s}^2
\][/tex]
3. Calculate the force:
Use the formula for force [tex]\( F = ma \)[/tex].
Substituting the values we have:
[tex]\[
F = 280 \times 0.5714 \approx 160 \, \text{Newtons}
\][/tex]
4. Choose the correct answer:
From the options given, the force required for the snowmobile to accelerate is approximately 160 N.
Thus, the correct answer is A. 160 N.
1. Understand the given data:
- Total mass with Sully on the snowmobile is 280 kilograms.
- Final velocity [tex]\( v \)[/tex] is 8 meters per second.
- Initial velocity [tex]\( \psi \)[/tex] is assumed to be 0 meters per second, meaning the snowmobile started from rest.
- Time [tex]\( t \)[/tex] taken to accelerate to the final velocity is 14 seconds.
2. Calculate the acceleration:
The formula for acceleration [tex]\( a \)[/tex] is:
[tex]\[
a = \frac{v - \psi}{t}
\][/tex]
Substituting the given values:
[tex]\[
a = \frac{8 - 0}{14} = \frac{8}{14} \approx 0.5714 \, \text{m/s}^2
\][/tex]
3. Calculate the force:
Use the formula for force [tex]\( F = ma \)[/tex].
Substituting the values we have:
[tex]\[
F = 280 \times 0.5714 \approx 160 \, \text{Newtons}
\][/tex]
4. Choose the correct answer:
From the options given, the force required for the snowmobile to accelerate is approximately 160 N.
Thus, the correct answer is A. 160 N.
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