Final answer:
The magnitude of the acceleration of the block is approximately 1.78 m/s². The coefficient of kinetic friction between the block and the incline is approximately 2.61 N. The speed of the block after sliding a distance of 2.00 m is approximately 3.56 m/s.
Step-by-step explanation:
To find the magnitude of the acceleration of the block, we can use the formula:
Acceleration (a) = (2 * distance) / (time^2)
Plugging in the given values, we have:
a = (2 * 2.00 m) / (1.50 s)^2
a ≈ 1.78 m/s²
To find the coefficient of kinetic friction between the block and the incline, we can use the formula:
Coefficient of friction (μ) = (Force of friction) / (Normal force)
Since the block is moving down the incline, the force of friction is in the opposite direction of the motion. Therefore, we can calculate the force of friction as:
Force of friction = mass * acceleration * sin(θ)
Plugging in the given values, we have:
Force of friction = 3.00 kg * 1.78 m/s² * sin(30.0°)
Force of friction ≈ 2.61 N
The magnitude of the frictional force acting on the block is 2.61 N.
To find the speed of the block after sliding a distance of 2.00 m, we can use the formula:
Final speed (v) = Initial velocity + (acceleration * distance)
Since the block starts from rest, the initial velocity is 0. Plugging in the given values, we have:
v = 0 + (1.78 m/s² * 2.00 m)
v ≈ 3.56 m/s