Final answer:
After 4 seconds, the ball is at a height of 29.6 meters. The average acceleration of a rocket traveling 400 meters in 5 seconds starting from rest is 160 m/s^2. A decreasing slope on a position vs. time graph indicates that the velocity is decreasing. Therefore, the correct option is B.
Step-by-step explanation:
For the ball launched at an initial velocity of 24 m/s from a height of 12 m, we can use the kinematic equation:
h(t) = h_0 + v_0t - (1/2)gt^2, where h(t) is the height after time t, h_0 is the initial height, v_0 is the initial velocity, g is the acceleration due to gravity (9.8 m/s^2), and t is the time. Plugging in the values, we get h(4) = 12 m + (24 m/s)(4 s) - (1/2)(9.8 m/s^2)(4 s)^2 = 12 m + 96 m - 78.4 m = 29.6 m. To find the average acceleration of a rocket that travels 400 m in 5 s from rest, we can use the equation d = (1/2)at^2, where d is the distance traveled, a is the acceleration, and t is the time. Rearranging for acceleration, we get a = 2d / t^2 = 2 × 400 m / (5 s)^2 = 160 m/s^2.
For a position versus time graph, if the slope is decreasing, it indicates that the velocity over time is also decreasing, so the correct answer is (B) Velocity is decreasing.