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Answer :
To solve this problem, we'll need to find the force exerted by the snowmobile to accelerate from an initial velocity to a final velocity. We can use the formula [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 the step-by-step process:
1. Understand the given information:
- Initial velocity ([tex]\( v_i \)[/tex]) = 10 meters/second
- Final velocity ([tex]\( v_f \)[/tex]) = 16 meters/second
- Time taken to accelerate = 10 seconds
- Total mass ([tex]\( m \)[/tex]) = 280 kilograms
2. Calculate the acceleration ([tex]\( a \)[/tex]):
Acceleration is defined as the change in velocity over time. You can use the formula:
[tex]\[
a = \frac{{v_f - v_i}}{t}
\][/tex]
Substituting 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 find 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 is 168 Newtons. Therefore, the correct answer is B. 168 N.
Here's the step-by-step process:
1. Understand the given information:
- Initial velocity ([tex]\( v_i \)[/tex]) = 10 meters/second
- Final velocity ([tex]\( v_f \)[/tex]) = 16 meters/second
- Time taken to accelerate = 10 seconds
- Total mass ([tex]\( m \)[/tex]) = 280 kilograms
2. Calculate the acceleration ([tex]\( a \)[/tex]):
Acceleration is defined as the change in velocity over time. You can use the formula:
[tex]\[
a = \frac{{v_f - v_i}}{t}
\][/tex]
Substituting 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 find 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 is 168 Newtons. Therefore, the correct answer is B. 168 N.
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