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Select the correct answer.

Sully is riding a snowmobile on a flat, snow-covered surface with a constant velocity of 10 meters/second. The total mass of the snowmobile, including Sully, is 280 kilograms. If Sully accelerates to a velocity of 16 meters/second over 10 seconds, what's the force exerted by the snowmobile to accelerate? Use [tex]F = ma[/tex], where [tex]a = \frac{\Delta v}{t}[/tex].

A. 160 N
B. 168 N
C. 248 N
D. 280 N
E. 324 N

Answer :

To find the force exerted by the snowmobile when Sully accelerates, we can follow these steps:

1. Identify the Given Values:
- Initial velocity ([tex]\(v_i\)[/tex]) = 10 meters/second
- Final velocity ([tex]\(v_f\)[/tex]) = 16 meters/second
- Total mass ([tex]\(m\)[/tex]) = 280 kilograms
- Time ([tex]\(t\)[/tex]) = 10 seconds

2. Calculate the Acceleration:
- Acceleration ([tex]\(a\)[/tex]) can be calculated using the formula:
[tex]\[
a = \frac{v_f - v_i}{t}
\][/tex]
- Substitute the given values:
[tex]\[
a = \frac{16 - 10}{10} = \frac{6}{10} = 0.6 \text{ meters/second}^2
\][/tex]

3. Calculate the Force:
- Use the equation for force:
[tex]\[
F = m \times a
\][/tex]
- Substitute the mass and the calculated acceleration:
[tex]\[
F = 280 \times 0.6 = 168 \text{ Newtons}
\][/tex]

So, the correct answer is B. 168 N.

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