Final answer:
The 10-kg box sliding down a frictionless 18-degree ramp has an acceleration of 3.03 m/s². It takes approximately 1.15 seconds for the box to slide 2 meters down the ramp.
Step-by-step explanation:
The question asks for the acceleration of a 10-kg box sliding down a frictionless 18-degree ramp and the time it takes to slide 2 meters down the ramp. To find acceleration, we use Newton's second law and the equation for acceleration on an inclined plane:
a = g × sin(θ)
Where g is the acceleration due to gravity (9.8 m/s²) and θ is the angle of inclination (18 degrees).
a = 9.8 m/s² × sin(18°)
= 9.8 × 0.309
= 3.03 m/s²
To find the time to slide 2 meters down the incline, we use kinematics:
s = ut + 0.5at²
Since initial velocity (u) is 0 (starts from rest),
2 = 0 × t + 0.5 × 3.03 × t²
t² = 2 / (0.5 × 3.03)
t = √(2 / 1.515)
t = 1.15 seconds
The acceleration of the box is 3.03 m/s², and it takes approximately 1.15 seconds to travel 2 meters down the ramp.