Final answer:
The rock took approximately 2.67 seconds to change its velocity to 8 m/s and an acceleration of 3 m/s². The final velocity of the car, after accelerating at 5 m/s² and traveling 46 meters, is approximately 21.65 m/s.
Step-by-step explanation:
For the first question, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity (which is 0 m/s since the rock was dropped from rest), a is the acceleration, and t is the time. In this case, v = 8 m/s, u = 0 m/s, and a = 3 m/s². Plugging in these values, we can solve for t: 8 = 0 + 3t. Simplifying, we get 3t = 8, so t = 8/3 = 2.67 seconds.
For the second question, we can use the equation v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled. In this case, v is the final velocity that we need to find, u is the initial velocity (which is 3 m/s), a is the acceleration (which is 5 m/s²), and s is the distance traveled (which is 46 meters). Plugging in these values, we get v² = 3² + 2(5)(46), so v² = 9 + 460 = 469. Taking the square root of both sides, we find that v ≈ 21.65 m/s.