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Final practice problems
8.1, 8.4, 8.5
4. The displacement x(t) of a particle as a function of time t is shown in the graph below.
(a) What is the average velocity during the following time intervals: 0  3 sec; 3  8 sec; 0
 6 sec.
(b) What is the instantaneous velocity at t = 1 sec, t = 3 sec and t = 8 sec.
5. A satellite of mass m moves in a circular orbit about the earth. The orbital radius is r
and the orbital velocity is v. The earth mass is M
e
and the gravitational constant is G.
(a) Find a relation between r and v by balancing the centripetal and gravitational
forces.
(b) Find the relation between the orbital T (time to travel once around the earth) and
the orbital radius r.
6. Two masses of respectively 4 and 8 Kg are connected by a string which passes over a
frictionless pulley (see figure).
(a) What is the tension T in the rope?
(b) What is the acceleration of either of the two masses?
(c) If the two masses start from rest, how far do they travel during the first second
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 Fall '07
 Miao

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