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Answer :
We are asked to determine the force required to accelerate the snowmobile, given:
- Total mass: [tex]$m = 280 \text{ kg}$[/tex]
- Initial velocity: [tex]$v_i = 10 \text{ m/s}$[/tex]
- Final velocity: [tex]$v_f = 16 \text{ m/s}$[/tex]
- Time interval: [tex]$t = 10 \text{ s}$[/tex]
Step 1: Calculate the acceleration
The formula to calculate the acceleration ([tex]$a$[/tex]) is:
[tex]$$
a = \frac{v_f - v_i}{t}
$$[/tex]
Substitute the given values:
[tex]$$
a = \frac{16 \text{ m/s} - 10 \text{ m/s}}{10 \text{ s}} = \frac{6 \text{ m/s}}{10 \text{ s}} = 0.6 \text{ m/s}^2
$$[/tex]
Step 2: Calculate the force
Recall Newton's second law:
[tex]$$
F = m \times a
$$[/tex]
Substitute the mass and the calculated acceleration:
[tex]$$
F = 280 \text{ kg} \times 0.6 \text{ m/s}^2 = 168 \text{ N}
$$[/tex]
Thus, the force exerted by the snowmobile to accelerate is [tex]$\boxed{168 \text{ N}}$[/tex].
Among the answer choices, this corresponds to:
B. 168 N.
- Total mass: [tex]$m = 280 \text{ kg}$[/tex]
- Initial velocity: [tex]$v_i = 10 \text{ m/s}$[/tex]
- Final velocity: [tex]$v_f = 16 \text{ m/s}$[/tex]
- Time interval: [tex]$t = 10 \text{ s}$[/tex]
Step 1: Calculate the acceleration
The formula to calculate the acceleration ([tex]$a$[/tex]) is:
[tex]$$
a = \frac{v_f - v_i}{t}
$$[/tex]
Substitute the given values:
[tex]$$
a = \frac{16 \text{ m/s} - 10 \text{ m/s}}{10 \text{ s}} = \frac{6 \text{ m/s}}{10 \text{ s}} = 0.6 \text{ m/s}^2
$$[/tex]
Step 2: Calculate the force
Recall Newton's second law:
[tex]$$
F = m \times a
$$[/tex]
Substitute the mass and the calculated acceleration:
[tex]$$
F = 280 \text{ kg} \times 0.6 \text{ m/s}^2 = 168 \text{ N}
$$[/tex]
Thus, the force exerted by the snowmobile to accelerate is [tex]$\boxed{168 \text{ N}}$[/tex].
Among the answer choices, this corresponds to:
B. 168 N.
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