(225 points) Two friends agree to test their physics background in 1D motion. John, is a
distance d ahead of Paul. Paul is driving at a constant, known velocity v0 when they start their experiment. At this moment, John accelerates from rest with his motorcycle in such a way that they only meet once at time tF at a distance xF from where Paul started the experiment. a) (50 points) Sketch x(t) and v(t) graphs for Paul's and John's motion as a function of time t in the same diagram, respectively in such a way that they only meet once at time tF at a distance xF. b) (30 points) What is the velocity of John starting from rest once he meets Paul in terms of v0 ? Hint: Keep in mind that Paul and John only meet once! c) (50 points) Show that the acceleration for John is given by: a = (v0)2/(2d) d) (50 points) Show that the time tF is given by: tF = (2d)/v0 e) (45 points) Show that the distance xF, i.e. the distance Paul traveled after he started counting the experiment, is given by: xF = 2� .