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Answer :
To solve this problem, we need to calculate the force exerted by a snowmobile to accelerate an object. We'll use the formula:
[tex]\[ F = m \times a \][/tex]
where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
Let's go through the steps:
1. Understand the given data:
- Mass ([tex]\( m \)[/tex]) = 2 kilograms
- Final velocity ([tex]\( v_f \)[/tex]) = 16 meters/second
- Time ([tex]\( t \)[/tex]) = 10 seconds
2. Calculate the acceleration ([tex]\( a \)[/tex]):
The acceleration can be calculated using the formula:
[tex]\[ a = \frac{\text{change in velocity}}{\text{time}} \][/tex]
Here, the change in velocity is 16 meters/second since it's accelerating from rest (starting from a velocity of 0).
[tex]\[ a = \frac{16 \, \text{meters/second}}{10 \, \text{seconds}} = 1.6 \, \text{meters/second}^2 \][/tex]
3. Calculate the force ([tex]\( F \)[/tex]):
Using the formula [tex]\( F = m \times a \)[/tex]:
[tex]\[ F = 2 \, \text{kg} \times 1.6 \, \text{meters/second}^2 = 3.2 \, \text{newtons} \][/tex]
Based on the choices given in the problem, none of them match the calculated force of 3.2 newtons. So, there might be an error in the listed options. It's important to double-check the problem statement and options provided.
[tex]\[ F = m \times a \][/tex]
where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
Let's go through the steps:
1. Understand the given data:
- Mass ([tex]\( m \)[/tex]) = 2 kilograms
- Final velocity ([tex]\( v_f \)[/tex]) = 16 meters/second
- Time ([tex]\( t \)[/tex]) = 10 seconds
2. Calculate the acceleration ([tex]\( a \)[/tex]):
The acceleration can be calculated using the formula:
[tex]\[ a = \frac{\text{change in velocity}}{\text{time}} \][/tex]
Here, the change in velocity is 16 meters/second since it's accelerating from rest (starting from a velocity of 0).
[tex]\[ a = \frac{16 \, \text{meters/second}}{10 \, \text{seconds}} = 1.6 \, \text{meters/second}^2 \][/tex]
3. Calculate the force ([tex]\( F \)[/tex]):
Using the formula [tex]\( F = m \times a \)[/tex]:
[tex]\[ F = 2 \, \text{kg} \times 1.6 \, \text{meters/second}^2 = 3.2 \, \text{newtons} \][/tex]
Based on the choices given in the problem, none of them match the calculated force of 3.2 newtons. So, there might be an error in the listed options. It's important to double-check the problem statement and options provided.
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