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Answer :
To solve this problem, we need to find the force exerted by the snowmobile to accelerate from a velocity of 10 meters/second to 16 meters/second over a period of 10 seconds. We'll use the formula for force, which is [tex]\( F = m \times a \)[/tex], where [tex]\( m \)[/tex] is the mass and [tex]\( a \)[/tex] is the acceleration.
Let's break it down step-by-step:
1. Identify the given values:
- Initial velocity ([tex]\( v_{\text{initial}} \)[/tex]) = 10 meters/second
- Final velocity ([tex]\( v_{\text{final}} \)[/tex]) = 16 meters/second
- Time ([tex]\( t \)[/tex]) = 10 seconds
- Mass ([tex]\( m \)[/tex]) = 280 kilograms
2. Calculate the acceleration ([tex]\( a \)[/tex]):
- Acceleration is given by the formula:
[tex]\[
a = \frac{v_{\text{final}} - v_{\text{initial}}}{t}
\][/tex]
- Plug in the values:
[tex]\[
a = \frac{16 \, \text{meters/second} - 10 \, \text{meters/second}}{10 \, \text{seconds}} = \frac{6}{10} = 0.6 \, \text{meters/second}^2
\][/tex]
3. Calculate the force ([tex]\( F \)[/tex]) using the formula:
- Force is calculated using:
[tex]\[
F = m \times a
\][/tex]
- Substitute the values:
[tex]\[
F = 280 \, \text{kilograms} \times 0.6 \, \text{meters/second}^2 = 168 \, \text{Newtons}
\][/tex]
Therefore, the force exerted by the snowmobile to accelerate is 168 Newtons. The correct answer is B. 168 N.
Let's break it down step-by-step:
1. Identify the given values:
- Initial velocity ([tex]\( v_{\text{initial}} \)[/tex]) = 10 meters/second
- Final velocity ([tex]\( v_{\text{final}} \)[/tex]) = 16 meters/second
- Time ([tex]\( t \)[/tex]) = 10 seconds
- Mass ([tex]\( m \)[/tex]) = 280 kilograms
2. Calculate the acceleration ([tex]\( a \)[/tex]):
- Acceleration is given by the formula:
[tex]\[
a = \frac{v_{\text{final}} - v_{\text{initial}}}{t}
\][/tex]
- Plug in the values:
[tex]\[
a = \frac{16 \, \text{meters/second} - 10 \, \text{meters/second}}{10 \, \text{seconds}} = \frac{6}{10} = 0.6 \, \text{meters/second}^2
\][/tex]
3. Calculate the force ([tex]\( F \)[/tex]) using the formula:
- Force is calculated using:
[tex]\[
F = m \times a
\][/tex]
- Substitute the values:
[tex]\[
F = 280 \, \text{kilograms} \times 0.6 \, \text{meters/second}^2 = 168 \, \text{Newtons}
\][/tex]
Therefore, the force exerted by the snowmobile to accelerate is 168 Newtons. The correct answer is B. 168 N.
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