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Answer :
To solve this problem and find the force exerted by the snowmobile, we can use the information about the change in velocity and the mass of the snowmobile with Sully. We will apply the formula for force: [tex]\( F = ma \)[/tex], where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
Here's a step-by-step solution:
1. Identify the Given Values:
- Initial velocity ([tex]\( v_i \)[/tex]) = 10 meters/second
- Final velocity ([tex]\( v_f \)[/tex]) = 16 meters/second
- Time ([tex]\( t \)[/tex]) = 10 seconds
- Total mass ([tex]\( m \)[/tex]) = 280 kilograms
2. Calculate the Acceleration ([tex]\( a \)[/tex]):
To find the acceleration, we use the formula for acceleration:
[tex]\[
a = \frac{v_f - v_i}{t}
\][/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]):
Now that we have the acceleration, we can calculate the force using the formula [tex]\( F = ma \)[/tex].
[tex]\[
F = 280 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 168 \, \text{N}
\][/tex]
The force exerted by the snowmobile to accelerate to the new velocity is 168 Newtons. Therefore, the correct answer is:
B. 168 N
Here's a step-by-step solution:
1. Identify the Given Values:
- Initial velocity ([tex]\( v_i \)[/tex]) = 10 meters/second
- Final velocity ([tex]\( v_f \)[/tex]) = 16 meters/second
- Time ([tex]\( t \)[/tex]) = 10 seconds
- Total mass ([tex]\( m \)[/tex]) = 280 kilograms
2. Calculate the Acceleration ([tex]\( a \)[/tex]):
To find the acceleration, we use the formula for acceleration:
[tex]\[
a = \frac{v_f - v_i}{t}
\][/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]):
Now that we have the acceleration, we can calculate the force using the formula [tex]\( F = ma \)[/tex].
[tex]\[
F = 280 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 168 \, \text{N}
\][/tex]
The force exerted by the snowmobile to accelerate to the new velocity is 168 Newtons. Therefore, the correct answer is:
B. 168 N
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