Yes, there are time limits for the Ph.D. program and for the Master's program.  According to the Graduate School Bulletin (2007/08 edition):

Masters Degree:

"All requirements for the master's degree must be completed within a six year period."  (p.55).

Ph.D. Degree:

• "All departments and other units offering Ph.D. programs must  set a maximum time limit within which a student ... is required to take the Qualifying Examination. That maximum time limit must not exceed eight semesters (preferably fewer) ..." (p. 55). The Department requirement is to pass the Qualifying Exam by the end of the fourth semester.
  
• "The dissertation must be completed within four years after a student has been admitted to candidacy for the degree" (p.55) [For your information: Students are admitted to candidacy by the Graduate School after they have passed the Qualifying Examination]

From these two statements one may conclude that there is an 8-year time limit for Ph.D. study at Vanderbilt.  Most students will finish in five to seven years.

Students whose grade point average (GPA) falls below 3.0 (i.e. below a B average) are placed on probation for one semester. If the student's performance does not improve during that semester, the Dean and Dept. Chair will decide whether to dismiss the student or continue the probation for another semester. If at the end of the second semester of probation the GPA is still below 3.0, the student is advised to withdraw or face dismissal. (Graduate School Bulletin, 2007/08 edition, p. 59.)

Students who earn a grade point average (GPA) of 2.0 or less during the first semester are subject to dismissal at the end of that semester. (Graduate School Bulletin,  2007/08 edition, p. 59.)

It is not possible to answer this question by only looking at the published Schedule of Courses for the Fall / Spring Semester. You must also consult the Graduate School Bulletin.  If the course is listed here, it counts towards graduate credit.

After the end of every semester you will receive a transcript of your academic record from the Graduate School. The transcript will state the grades you have earned and other vital information, including:

• EHRS (Earned hours): The total number of hours of graduate study in your field. You need at least 72 hours to earn a Ph.D.
• QHRS (Quality hours): The hours of "formal course work", i.e. lectures and seminars that count toward the Ph.D. degree.  The required number varies by department.  For the Department of Physics and Astronomy, you need at least 36 hours.
• AHRS (attempted hours): The number of credit hours that you have attempted.
• Qualifying Exam and Degrees Awarded:  If you pass the Qualifying Exam, your Ph.D. Committee Chair will inform the Graduate School (as required).  Your transcript will state that you have passed.  It will also state degrees you have been awarded. If your transcript does not state these two thinhgs, it means that the Graduate School does not know about it, and you should take corrective action.

Only graduate courses with a B or better can be transfered .  For a master's degree, a maximum of six hours may be transferred.  For a Ph.D. degree, a maximum of 48 hours may be transferred. Grades earned on transfer credit  WILL affect your VU Graduate School Grade Point Average (GPA), if courses transfered are to be counted as didactic hours. (Seminar and research work would NOT count  as didactic hours.)

The following procedures are based on the Bulletin of the Graduate School and Department regulations.

STEP 1:
The current Ph.D. regulations were approved on November 12, 2001.  If you began your Ph.D. degree before this date, you are subject to the old Ph.D. regulations.  The new Ph.D. regulations are: after having passed the written Core Examination, are required to set up their Ph.D. Committee and schedule the time of the Qualifying Examination no later than the end of the 8th semester (preferably earlier) and may be attempted no more than twice (see Graduate School Bulletin 2007/08, p. 55).  Students should consult their adviser regarding the appointment of the Committee which must contain at least four members of the graduate faculty. The Ph.D. committee members should be chosen from different research areas. The Ph.D. adviser will usually chair the committee.  Ask your Ph.D. adviser to write a brief memo to the Director of Graduate Studies (DGS) who must approve the suggested committee members. The DGS shall forward their recommendation to the Dean of the Graduate School.

STEP 2:
Make sure that you, your adviser and all committee members have received an official letter of the Ph.D. committee appointment from the Graduate Dean. This typically takes two weeks after the DGS's recommendation has been received by the Graduate School.

STEP 3:
After your Ph.D. committee has been officially appointed, you must schedule the date of your  Qualifying Exam.  If you enrolled during the Spring 2001 or before the rules may differ slightly.  Contact the Graduate School for more information.  For everyone, the Graduate School must be notified of the time and place of the Qualifying Examination at least two weeks in advance.

STEP 4:
The purpose of the Qualifying Exam is to test the student's knowledge of the field of specialization. Please discuss with your Ph.D adviser and / or your committee members what you are expected to know and the format of your presentation. You should schedule a meeting with your committee, at least one month prior to you Exam date, for the purpose of reviewing the scope of the exam.

STEP 5:
The Ph.D. adviser will inform the DGS and then the Dean of the Graduate School, in writing of the result of the Qualifying Exam. He/She will use the "Results of Qualifying Examination" Form which is available from the Graduate School or the Director of Graduate Studies. This form is to be signed by all Ph.D. committee members. A copy should be given to the Director of Graduate Studies for placement into the student's Department file.

For more details on requirements for the Ph.D. degree please contact The Graduate School.

The Graduate School has detailed rules for the preparation of the Ph.D. thesis and thesis defense (as well as the rules pertaining to the M.S. degree).  The main point to be aware of is that the Chair of the Ph.D. committee shall notify the Dean of the Graduate School in writing no later than two weeks prior to the examination of the place and time of the examination and the title of the dissertation. The Dean will then formally notify all committee members. (The main purpose of the two week advance notice is to give sufficient time for announcement of the Ph.D. Defense in the Vanderbilt Calendar; the Defense is open to the whole university community). The result of the Examination must be reported by the Ph.D. committee Chair to the Graduate Dean immediately after the examination.

Two copies of the approved dissertation, bearing original signatures of not less than a majority of the Ph.D. committee, accompanied by two copies of an abstract of not more than three hundred fifty words and signed by the student's adviser, must be registered in the Dean's office no later than two weeks before the end of the term in which the student expects to receive the degree. A candidate who expects to graduate in May must submit the dissertation to the Graduate School no later than April 1.

• Earn at least 42 credit hours of graduate study in physics, with B average or better.  Four of the 42 hours must be in Phys-399 (Ph.D. dissertation research).
• Pass the Ph.D. Core Examintation. 
• Present a brief report to the Ph.D. committee on his/her research experience.

• Ph.D. committee must have been officially appointed by the Graduate School in consultation with the Department Chair.
• The candidate must have successfully completed at least 4 hours of Ph.D. dissertation research and presented a report to the Ph.D. committee.
• Only the Ph.D. adviser or a member of the Ph.D. committee can certify that ALL of the conditions have been met.