Final answer:
The magnitude of the acceleration along the incline is approximately 4.15 m/s². The marble goes approximately 29.48 meters down the incline in 3.75 seconds.
Step-by-step explanation:
(a) To find the magnitude of the acceleration along the incline, we can use the equation
a = g * sin(θ)
where g is the acceleration due to gravity (9.8 m/s²) and θ is the angle of the incline (25°). Substituting the values in, we get
a = 9.8 * sin(25°) ≈ 4.15 m/s²
Therefore, the magnitude of the acceleration along the incline is approximately 4.15 m/s².
(b) To find how far down the incline the marble goes in 3.75 s, we can use the equation
s = ut + ½at²
where s is the distance, u is the initial velocity (which is 0 in this case), t is the time (3.75 s), and a is the acceleration (4.15 m/s²). Substituting the values in, we get
s = 0 + 0.5 * 4.15 * (3.75)² ≈ 29.48 m
Therefore, the marble goes approximately 29.48 meters down the incline in 3.75 seconds.