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Answer :
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1. Identify the Initial and Final Velocities:
- Initial velocity ([tex]\(v_i\)[/tex]) of the snowmobile: 10 meters/second.
- Final velocity ([tex]\(v_f\)[/tex]) of the snowmobile: 16 meters/second.
2. Calculate the Change in Velocity:
- Change in velocity ([tex]\(\Delta v\)[/tex]) is given by the formula:
[tex]\[
\Delta v = v_f - v_i
\][/tex]
- Substituting the values:
[tex]\[
\Delta v = 16 \, \text{m/s} - 10 \, \text{m/s} = 6 \, \text{m/s}
\][/tex]
3. Determine the Time Taken for Acceleration:
- Time ([tex]\(t\)[/tex]) taken to accelerate: 10 seconds.
4. Calculate the Acceleration:
- Acceleration ([tex]\(a\)[/tex]) is calculated using the formula:
[tex]\[
a = \frac{\Delta v}{t}
\][/tex]
- Substituting the values:
[tex]\[
a = \frac{6 \, \text{m/s}}{10 \, \text{s}} = 0.6 \, \text{m/s}^2
\][/tex]
5. Find the Mass of the Snowmobile:
- Total mass ([tex]\(m\)[/tex]) of the snowmobile including Sully: 230 kilograms.
6. Calculate the Force Exerted by the Snowmobile:
- Use Newton's second law of motion:
[tex]\[
F = ma
\][/tex]
- Substituting the known values:
[tex]\[
F = 230 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 138 \, \text{N}
\][/tex]
Therefore, the force exerted by the snowmobile to accelerate is 138 Newtons.
It seems that there has been an error in the choice options, as 138 Newtons is not listed. Please check if there might have been a misprint in the options provided.
1. Identify the Initial and Final Velocities:
- Initial velocity ([tex]\(v_i\)[/tex]) of the snowmobile: 10 meters/second.
- Final velocity ([tex]\(v_f\)[/tex]) of the snowmobile: 16 meters/second.
2. Calculate the Change in Velocity:
- Change in velocity ([tex]\(\Delta v\)[/tex]) is given by the formula:
[tex]\[
\Delta v = v_f - v_i
\][/tex]
- Substituting the values:
[tex]\[
\Delta v = 16 \, \text{m/s} - 10 \, \text{m/s} = 6 \, \text{m/s}
\][/tex]
3. Determine the Time Taken for Acceleration:
- Time ([tex]\(t\)[/tex]) taken to accelerate: 10 seconds.
4. Calculate the Acceleration:
- Acceleration ([tex]\(a\)[/tex]) is calculated using the formula:
[tex]\[
a = \frac{\Delta v}{t}
\][/tex]
- Substituting the values:
[tex]\[
a = \frac{6 \, \text{m/s}}{10 \, \text{s}} = 0.6 \, \text{m/s}^2
\][/tex]
5. Find the Mass of the Snowmobile:
- Total mass ([tex]\(m\)[/tex]) of the snowmobile including Sully: 230 kilograms.
6. Calculate the Force Exerted by the Snowmobile:
- Use Newton's second law of motion:
[tex]\[
F = ma
\][/tex]
- Substituting the known values:
[tex]\[
F = 230 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 138 \, \text{N}
\][/tex]
Therefore, the force exerted by the snowmobile to accelerate is 138 Newtons.
It seems that there has been an error in the choice options, as 138 Newtons is not listed. Please check if there might have been a misprint in the options provided.
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