Final answer:
The displacement of the rocket over 8 seconds with acceleration from 51 m/s to 88 m/s is calculated to be 556 meters, which doesn't match any provided options, indicating a potential typo or miscalculation.
Step-by-step explanation:
The student's question involves calculating the displacement of a rocket undergoing constant acceleration. The rocket's initial velocity (u) is 51 m/s and the final velocity (v) is 88 m/s, with the time (t) taken for this change being 8 seconds. Using the kinematic equation for displacement (s) where acceleration (a) is constant, which is s = ut + 0.5at², first, we need to find the acceleration using a = (v - u) / t.
Acceleration is found to be a = (88 m/s - 51 m/s) / 8 s which equals 4.625 m/s². Plugging the values into the displacement equation, we get s = 51 m/s × 8 s + 0.5 × 4.625 m/s² × (8 s)².
After performing the calculations, the displacement is found to be 556 m. However, since none of the options match this value, there may have been a typo or a miscalculation in the question or the available answers.