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Select the correct answer.

Suly 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 Suly, is 280 kilograms. If Suly 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].

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

Answer :

To solve the problem of finding the force exerted by the snowmobile to accelerate, we can follow these steps:

1. Identify the variables:
- Initial velocity ([tex]\(u\)[/tex]): 10 meters/second
- Final velocity ([tex]\(v\)[/tex]): 16 meters/second
- Time duration ([tex]\(t\)[/tex]): 10 seconds
- Mass ([tex]\(m\)[/tex]): 280 kilograms

2. Calculate the acceleration ([tex]\(a\)[/tex]):
- The formula for acceleration is given by:
[tex]\[
a = \frac{\text{{final velocity}} - \text{{initial velocity}}}{\text{{time}}}
\][/tex]
- Plug in the values:
[tex]\[
a = \frac{16 - 10}{10} = \frac{6}{10} = 0.6 \text{ meters/second}^2
\][/tex]

3. Calculate the force ([tex]\(F\)[/tex]):
- Using the formula [tex]\(F = m \times a\)[/tex], where:
- [tex]\(F\)[/tex] is the force,
- [tex]\(m\)[/tex] is the mass,
- [tex]\(a\)[/tex] is the acceleration.
- Substitute the known values:
[tex]\[
F = 280 \times 0.6 = 168 \text{ Newtons}
\][/tex]

Therefore, the force exerted by the snowmobile to accelerate is 168 Newtons. The correct answer is B) 168 N.

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