Question

A marble rolls down an incline at 30° from rest. What is its acceleration? How far does it go in 3.0 s?

a) 4.9 m/s², 7.35 m
b) 5.7 m/s², 10.8 m
c) 6.5 m/s², 15.5 m
d) 8.2 m/s², 22.05 m

Answer 1

The acceleration of the marble rolling down the incline at 30° is 4.9 m/s² and it travels a distance of 22.05 m in 3 seconds.

Step-by-step explanation:

To calculate the acceleration of the marble rolling down an incline at 30°, we can use the formula:

acceleration = g * sin(θ)

Where g is the acceleration due to gravity (approximately 9.8 m/s²) and θ is the angle of the incline (30°).

Substituting the values into the formula:

acceleration = 9.8 m/s² * sin(30°) = 4.9 m/s²

To calculate how far the marble goes in 3 seconds, we can use the formula:

distance = 0.5 * acceleration * time²

Substituting the values into the formula:

distance = 0.5 * 4.9 m/s² * (3 s)² = 22.05 m

Therefore, the correct answer is (d) 8.2 m/s², 22.05 m.

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