Let's solve the problem step-by-step.
We are given:
- The mass of the snowmobile including Sully ([tex]\(m\)[/tex]) = 280 kg
- The initial velocity ([tex]\(u\)[/tex]) = 10 m/s
- The final velocity ([tex]\(v\)[/tex]) = 16 m/s
- The time taken to accelerate ([tex]\(t\)[/tex]) = 10 seconds
First, we need to find the acceleration ([tex]\(a\)[/tex]). The formula for acceleration is:
[tex]\[ a = \frac{v - u}{t} \][/tex]
Substitute the given values:
[tex]\[ a = \frac{16 \, \text{m/s} - 10 \, \text{m/s}}{10 \, \text{s}} \][/tex]
[tex]\[ a = \frac{6 \, \text{m/s}}{10 \, \text{s}} \][/tex]
[tex]\[ a = 0.6 \, \text{m/s}^2 \][/tex]
Next, we use the formula [tex]\( F = m \times a \)[/tex] to find the force ([tex]\(F\)[/tex]).
Given:
- [tex]\( m = 280 \, \text{kg} \)[/tex]
- [tex]\( a = 0.6 \, \text{m/s}^2 \)[/tex]
Substitute the values into the formula:
[tex]\[ F = 280 \, \text{kg} \times 0.6 \, \text{m/s}^2 \][/tex]
[tex]\[ F = 168 \, \text{N} \][/tex]
Therefore, the correct answer is:
B. 168 N
