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Answer :
We are given the following information:
- Initial velocity: $v_i = 10 \, \text{m/s}$
- Final velocity: $v_f = 16 \, \text{m/s}$
- Time: $t = 10 \, \text{s}$
- Mass: $m = 280 \, \text{kg}$
**Step 1: Calculate the acceleration**
The acceleration ($a$) is determined by the change in velocity over time:
$$
a = \frac{v_f - v_i}{t} = \frac{16 - 10}{10} = \frac{6}{10} = 0.6 \, \text{m/s}^2.
$$
**Step 2: Calculate the force required for the acceleration**
Using Newton's second law, the force ($F$) is given by:
$$
F = m \times a.
$$
Substitute the values for mass and acceleration:
$$
F = 280 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 168 \, \text{N}.
$$
Thus, the force exerted by the snowmobile to accelerate is $\boxed{168 \, \text{N}}$.
- Initial velocity: $v_i = 10 \, \text{m/s}$
- Final velocity: $v_f = 16 \, \text{m/s}$
- Time: $t = 10 \, \text{s}$
- Mass: $m = 280 \, \text{kg}$
**Step 1: Calculate the acceleration**
The acceleration ($a$) is determined by the change in velocity over time:
$$
a = \frac{v_f - v_i}{t} = \frac{16 - 10}{10} = \frac{6}{10} = 0.6 \, \text{m/s}^2.
$$
**Step 2: Calculate the force required for the acceleration**
Using Newton's second law, the force ($F$) is given by:
$$
F = m \times a.
$$
Substitute the values for mass and acceleration:
$$
F = 280 \, \text{kg} \times 0.6 \, \text{m/s}^2 = 168 \, \text{N}.
$$
Thus, the force exerted by the snowmobile to accelerate is $\boxed{168 \, \text{N}}$.
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