Final answer:
The work done on the 8 kg ball over the 5 second interval, as it changes from 2 m/s in the positive direction to 8 m/s in the negative direction, is 240 joules.
Step-by-step explanation:
The work done on an 8 kg ball that changes its speed from 2 m/s in the positive direction to 8 m/s in the negative direction during a 5 second interval can be calculated using the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. We first find the initial and final kinetic energies (KE) using the formula KE = 0.5 * m * v2, where m is the mass and v is the velocity. Then, we calculate the work done (W) as the difference between the final and initial kinetic energies.
The initial kinetic energy is KEi = 0.5 * 8 kg * (2 m/s)2 = 16 J, and the final kinetic energy is KEf = 0.5 * 8 kg * (8 m/s)2 = 256 J. Therefore, the work done is W = KEf - KEi = 256 J - 16 J = 240 J.