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Answer :
To solve this problem, we need to find the force exerted by the snowmobile to accelerate. We can use Newton's second law of motion, which states that force equals mass times acceleration, or [tex]\( F = m \times a \)[/tex].
Here's how to determine it step-by-step:
1. Identify the known 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
- Mass ([tex]\( m \)[/tex]) = 280 kilograms
2. Find the acceleration ([tex]\( a \)[/tex]):
- The formula for acceleration is [tex]\( a = \frac{v_f - v_i}{t} \)[/tex].
- Substitute the known 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]):
- Use the formula [tex]\( F = m \times a \)[/tex].
- Substitute the values for mass and acceleration:
[tex]\[
F = 280 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 168 \, \text{N}
\][/tex]
Therefore, the force exerted by the snowmobile to accelerate is 168 Newtons.
The correct answer is:
B. 168 N
Here's how to determine it step-by-step:
1. Identify the known 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
- Mass ([tex]\( m \)[/tex]) = 280 kilograms
2. Find the acceleration ([tex]\( a \)[/tex]):
- The formula for acceleration is [tex]\( a = \frac{v_f - v_i}{t} \)[/tex].
- Substitute the known 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]):
- Use the formula [tex]\( F = m \times a \)[/tex].
- Substitute the values for mass and acceleration:
[tex]\[
F = 280 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 168 \, \text{N}
\][/tex]
Therefore, the force exerted by the snowmobile to accelerate is 168 Newtons.
The correct answer is:
B. 168 N
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