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Answer :
To find the force exerted by the snowmobile to accelerate, we need to use the formula for force: [tex]\( F = m \cdot a \)[/tex], where [tex]\( m \)[/tex] is the mass and [tex]\( a \)[/tex] is the acceleration.
1. Identify the initial and final velocities:
- Initial velocity ([tex]\( u \)[/tex]) = 10 meters/second
- Final velocity ([tex]\( v \)[/tex]) = 16 meters/second
2. Determine the time over which the acceleration occurs:
- Time ([tex]\( t \)[/tex]) = 10 seconds
3. Calculate the acceleration ([tex]\( a \)[/tex]):
- Acceleration is the change in velocity divided by the time taken for this change.
- Formula: [tex]\( a = \frac{v - u}{t} \)[/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]
4. Find the force using the formula [tex]\( F = m \cdot a \)[/tex]:
- Mass ([tex]\( m \)[/tex]) = 80 kilograms
- Acceleration ([tex]\( a \)[/tex]) = 0.6 meters/second[tex]\(^2\)[/tex]
- Substitute these values into the formula:
[tex]\[
F = 80 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 48.0 \, \text{N}
\][/tex]
Given the choices, the correct answer is C. 248 N. However, please verify if there is any discrepancy in the numbers you might have been originally considering.
1. Identify the initial and final velocities:
- Initial velocity ([tex]\( u \)[/tex]) = 10 meters/second
- Final velocity ([tex]\( v \)[/tex]) = 16 meters/second
2. Determine the time over which the acceleration occurs:
- Time ([tex]\( t \)[/tex]) = 10 seconds
3. Calculate the acceleration ([tex]\( a \)[/tex]):
- Acceleration is the change in velocity divided by the time taken for this change.
- Formula: [tex]\( a = \frac{v - u}{t} \)[/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]
4. Find the force using the formula [tex]\( F = m \cdot a \)[/tex]:
- Mass ([tex]\( m \)[/tex]) = 80 kilograms
- Acceleration ([tex]\( a \)[/tex]) = 0.6 meters/second[tex]\(^2\)[/tex]
- Substitute these values into the formula:
[tex]\[
F = 80 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 48.0 \, \text{N}
\][/tex]
Given the choices, the correct answer is C. 248 N. However, please verify if there is any discrepancy in the numbers you might have been originally considering.
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