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Answer :
To solve the problem of finding the force exerted by the snowmobile when it accelerates, we can follow these steps:
1. Understanding the Problem:
- Sully is initially riding at a velocity of 10 meters/second.
- He accelerates to a velocity of 16 meters/second over a time period of 10 seconds.
- The total mass of Sully and the snowmobile is 280 kilograms.
2. Find the Change in Velocity:
- Initial velocity ([tex]\(v_i\)[/tex]) = 10 meters/second
- Final velocity ([tex]\(v_f\)[/tex]) = 16 meters/second
- Change in velocity ([tex]\(\Delta v\)[/tex]) = [tex]\(v_f - v_i = 16 - 10 = 6\)[/tex] meters/second
3. Calculate the Acceleration:
- Acceleration ([tex]\(a\)[/tex]) is calculated by the formula: [tex]\(a = \frac{\Delta v}{\Delta t}\)[/tex], where [tex]\(\Delta t\)[/tex] is the time taken for the change.
- Substitute the values: [tex]\(\Delta v = 6\)[/tex] meters/second, [tex]\(\Delta t = 10\)[/tex] seconds.
- [tex]\(a = \frac{6 \, \text{m/s}}{10 \, \text{s}} = 0.6 \, \text{m/s}^2\)[/tex].
4. Apply the Formula for Force:
- Use Newton's second law, [tex]\(F = m \cdot a\)[/tex], where [tex]\(m\)[/tex] is mass and [tex]\(a\)[/tex] is acceleration.
- Mass ([tex]\(m\)[/tex]) = 280 kilograms
- Acceleration ([tex]\(a\)[/tex]) = 0.6 meters/second²
- [tex]\(F = 280 \, \text{kg} \cdot 0.6 \, \text{m/s}^2 = 168 \, \text{N}\)[/tex].
5. Answer:
- The force exerted by the snowmobile to accelerate is 168 Newtons.
Therefore, the correct answer is B. 168 N.
1. Understanding the Problem:
- Sully is initially riding at a velocity of 10 meters/second.
- He accelerates to a velocity of 16 meters/second over a time period of 10 seconds.
- The total mass of Sully and the snowmobile is 280 kilograms.
2. Find the Change in Velocity:
- Initial velocity ([tex]\(v_i\)[/tex]) = 10 meters/second
- Final velocity ([tex]\(v_f\)[/tex]) = 16 meters/second
- Change in velocity ([tex]\(\Delta v\)[/tex]) = [tex]\(v_f - v_i = 16 - 10 = 6\)[/tex] meters/second
3. Calculate the Acceleration:
- Acceleration ([tex]\(a\)[/tex]) is calculated by the formula: [tex]\(a = \frac{\Delta v}{\Delta t}\)[/tex], where [tex]\(\Delta t\)[/tex] is the time taken for the change.
- Substitute the values: [tex]\(\Delta v = 6\)[/tex] meters/second, [tex]\(\Delta t = 10\)[/tex] seconds.
- [tex]\(a = \frac{6 \, \text{m/s}}{10 \, \text{s}} = 0.6 \, \text{m/s}^2\)[/tex].
4. Apply the Formula for Force:
- Use Newton's second law, [tex]\(F = m \cdot a\)[/tex], where [tex]\(m\)[/tex] is mass and [tex]\(a\)[/tex] is acceleration.
- Mass ([tex]\(m\)[/tex]) = 280 kilograms
- Acceleration ([tex]\(a\)[/tex]) = 0.6 meters/second²
- [tex]\(F = 280 \, \text{kg} \cdot 0.6 \, \text{m/s}^2 = 168 \, \text{N}\)[/tex].
5. Answer:
- The force exerted by the snowmobile to accelerate is 168 Newtons.
Therefore, the correct answer is B. 168 N.
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