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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 is 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 solve the problem of finding the force exerted by the snowmobile, we can follow these simple steps:

1. Understand the Initial Situation:
- Sully is riding a snowmobile with an initial velocity of 10 meters per second.
- The snowmobile, including Sully, has a total mass of 280 kilograms.

2. Determine the Change in Velocity:
- Sully accelerates to a final velocity of 16 meters per second.
- The change in velocity ([tex]\( \Delta v \)[/tex]) is calculated as:
[tex]\[ \Delta v = \text{final velocity} - \text{initial velocity} = 16 \, \text{m/s} - 10 \, \text{m/s} = 6 \, \text{m/s} \][/tex]

3. Calculate the Acceleration:
- The acceleration ([tex]\( a \)[/tex]) can be found using the formula:
[tex]\[ a = \frac{\Delta v}{t} \][/tex]
- Given that Sully takes 10 seconds to accelerate, the acceleration is:
[tex]\[ a = \frac{6 \, \text{m/s}}{10 \, \text{s}} = 0.6 \, \text{m/s}^2 \][/tex]

4. Calculate the Force:
- 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,
- We find the force exerted by the snowmobile:
[tex]\[ F = 280 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 168 \, \text{N} \][/tex]

Based on these calculations, the correct answer is 168 N. Therefore, the force exerted by the snowmobile to accelerate to the new velocity is option B. 168 N.

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