Final answer:
The acceleration of the roller coaster is 3.35 m/s², and the time it takes to reach the bottom of the 30.0 m long track, assuming no friction, is approximately 4.24 seconds.
Step-by-step explanation:
Roller Coaster Physics Problem
To determine the acceleration of the roller coaster car and the time elapsed before it reaches the bottom of the track, we can use the principles of physics that govern motion on an inclined plane. Since there is no friction, the only force causing acceleration is the component of gravity along the incline.
(a) The acceleration of the car can be found using the formula a = g × sin(θ), where g is the acceleration due to gravity (9.81 m/s2) and θ is the angle of the incline. Plugging in the values, a = 9.81 m/s2 × sin(20.0°), we get:
Acceleration (a) = 3.35 m/s2
(b) To find the time elapsed, we can use the kinematic equation d = ½(a)t2, where d is the distance along the incline, and t is the time. Solving for t with d = 30.0 m and the previously calculated acceleration, we get:
Time (t) = √(2d/a), which equals approximately 4.24 seconds.