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Answer :
Final answer:
The question is from a Physics subject, for the High School level, involving a block sliding down an inclined plane. Using kinematic equations and the gravitational acceleration component along the incline, the final velocity of the block is calculated as approximately 4.09 m/s.
Explanation:
The subject of this question is Physics, and it is suited for a High School level student. The problem involves a 3.50-kg block that slides down a 30.0° incline, covering a distance of 1.70 m in 1.00 s from rest. To find the final velocity, we can use the kinematic equation:
v² = u² + 2as
where v is the final velocity, u is the initial velocity (which is 0 since it starts from rest), a is the acceleration, and s is the distance traveled.
To find the acceleration, we use the component of gravitational acceleration along the incline, which is g sin(θ). With the angle of incline (θ) being 30° and gravitational acceleration (g) approximately 9.81 m/s², we get:
a = g sin(30°) = 9.81 × 0.5 = 4.905 m/s²
Now we can calculate the final velocity:
v = √(0 + 2 × 4.905 m/s² × 1.70 m)
v = √(16.7075 m²/s²)
v = 4.09 m/s
This value is not in the provided options (a to d), which suggests that there might be an error in the provided choices or that additional factors such as friction may need to be considered in a more detailed version of the problem.
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