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Answer :
To solve this problem, we need to find the force exerted by the snowmobile to accelerate from 10 meters/second to 16 meters/second over 10 seconds. To do this, we'll use the formula for force: [tex]\( F = m \cdot a \)[/tex].
Here are the steps:
1. Identify the Variables:
- Initial velocity ([tex]\( u \)[/tex]) = 10 meters/second.
- Final velocity ([tex]\( v \)[/tex]) = 16 meters/second.
- Time ([tex]\( t \)[/tex]) = 10 seconds.
- Total mass ([tex]\( m \)[/tex]) = 280 kilograms.
2. Calculate Acceleration ([tex]\( a \)[/tex]):
- Acceleration is the change in velocity divided by the time taken. The formula is:
[tex]\[
a = \frac{v - u}{t}
\][/tex]
- Substitute the given values:
[tex]\[
a = \frac{16 \, \text{m/s} - 10 \, \text{m/s}}{10 \, \text{s}} = \frac{6 \, \text{m/s}}{10 \, \text{s}} = 0.6 \, \text{m/s}^2
\][/tex]
3. Calculate the Force ([tex]\( F \)[/tex]):
- Using the formula [tex]\( F = m \cdot a \)[/tex]:
[tex]\[
F = 280 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 168 \, \text{N}
\][/tex]
Therefore, the force exerted by the snowmobile is 168 N. The correct answer is B. 168 N.
Here are the steps:
1. Identify the Variables:
- Initial velocity ([tex]\( u \)[/tex]) = 10 meters/second.
- Final velocity ([tex]\( v \)[/tex]) = 16 meters/second.
- Time ([tex]\( t \)[/tex]) = 10 seconds.
- Total mass ([tex]\( m \)[/tex]) = 280 kilograms.
2. Calculate Acceleration ([tex]\( a \)[/tex]):
- Acceleration is the change in velocity divided by the time taken. The formula is:
[tex]\[
a = \frac{v - u}{t}
\][/tex]
- Substitute the given values:
[tex]\[
a = \frac{16 \, \text{m/s} - 10 \, \text{m/s}}{10 \, \text{s}} = \frac{6 \, \text{m/s}}{10 \, \text{s}} = 0.6 \, \text{m/s}^2
\][/tex]
3. Calculate the Force ([tex]\( F \)[/tex]):
- Using the formula [tex]\( F = m \cdot a \)[/tex]:
[tex]\[
F = 280 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 168 \, \text{N}
\][/tex]
Therefore, the force exerted by the snowmobile is 168 N. The correct answer is B. 168 N.
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