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Answer :
To solve the problem of finding the force exerted by Sully's snowmobile when accelerating, we can follow these steps:
1. Identify the Given Information:
- Initial velocity ([tex]\( u \)[/tex]) = 10 meters/second
- Final velocity ([tex]\( v \)[/tex]) = 16 meters/second
- Time ([tex]\( t \)[/tex]) during which the acceleration occurs = 10 seconds
- Total mass of Sully and the snowmobile = 280 kilograms
2. Calculate Acceleration:
Acceleration ([tex]\( a \)[/tex]) is the change in velocity divided by the time taken for that change. The formula to find the acceleration is:
[tex]\[
a = \frac{v-u}{t}
\][/tex]
Substituting the known values:
[tex]\[
a = \frac{16 \, \text{m/s} - 10 \, \text{m/s}}{10 \, \text{seconds}} = \frac{6}{10} = 0.6 \, \text{m/s}^2
\][/tex]
3. Calculate the Force:
Using Newton's second law of motion, the force ([tex]\( F \)[/tex]) exerted can be calculated using the formula:
[tex]\[
F = m \times a
\][/tex]
where [tex]\( m \)[/tex] is the mass and [tex]\( a \)[/tex] is the acceleration.
Substituting the known values:
[tex]\[
F = 280 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 168 \, \text{N}
\][/tex]
Therefore, the force exerted by the snowmobile while accelerating is 168 N. Thus, the correct answer is B. 168 N.
1. Identify the Given Information:
- Initial velocity ([tex]\( u \)[/tex]) = 10 meters/second
- Final velocity ([tex]\( v \)[/tex]) = 16 meters/second
- Time ([tex]\( t \)[/tex]) during which the acceleration occurs = 10 seconds
- Total mass of Sully and the snowmobile = 280 kilograms
2. Calculate Acceleration:
Acceleration ([tex]\( a \)[/tex]) is the change in velocity divided by the time taken for that change. The formula to find the acceleration is:
[tex]\[
a = \frac{v-u}{t}
\][/tex]
Substituting the known values:
[tex]\[
a = \frac{16 \, \text{m/s} - 10 \, \text{m/s}}{10 \, \text{seconds}} = \frac{6}{10} = 0.6 \, \text{m/s}^2
\][/tex]
3. Calculate the Force:
Using Newton's second law of motion, the force ([tex]\( F \)[/tex]) exerted can be calculated using the formula:
[tex]\[
F = m \times a
\][/tex]
where [tex]\( m \)[/tex] is the mass and [tex]\( a \)[/tex] is the acceleration.
Substituting the known values:
[tex]\[
F = 280 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 168 \, \text{N}
\][/tex]
Therefore, the force exerted by the snowmobile while accelerating is 168 N. Thus, the correct answer is B. 168 N.
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