4 9 points Let v(t) represent the velocity of a photon t seconds after it is emitted from a light source. Answer the following questions: a. If the photon is unobstructed, then v(t) = c, where c ~ 3.00 x 10 m/s is the speed of light. Use the net change theorem set up the integral that represents the displacement of the particle T' seconds after it is emitted. You do not have to evaluate the integral. b. Determine whether the following improper integral converges or diverges. If it converges, give its value. If it diverges, specify whether it diverges to co or -0o. So cat c. Interpret your answer to part b in the context of this problem. (What does the integral mean? What does the answer to part b tell you about the photon?) d. Now suppose the photon is obstructed in some way, and its velocity is given by v (t) = C ( t + 1 ) 2 Determine whether the following improper integral converges or diverges. If it converges, give its value. If it diverges, specify whether it diverges to co or -DO. C (t + 1)2 dt e. Interpret your answer to part d in the context of this problem. (What does the integral mean? What does the answer to part d tell you about the photon?) Note: you can just write c during your calculations, rather than using the numerical estimate of 3.00 X 10m/s. Additionally, remember that c is a constant