Practice Exam (Chap. 1, 2, 3) 1. Do NOT write the answer alone. Indicate what you are doing. You cannot have full credit for merely writing down the answer. 2. You can have partial credit if you can show that you are in the right track. Therefore, your answer should be neatly written and well organized to understand. 3. Express the answer with the information given in the problem. 4. You cannot use your textbook or notebook, but you can use a calculator. This is a practice exam. Several problems are collected from the exams of other classes. By solving this exam, you can figure out the level and type of problems you will have in exams. Try to solve the problems first, and then check your answer with the solution. You will have 4-5 problems in the exam but this practice exam contains 6 problems. Some topics are not covered by this practice exam, but the exam may cover those topics. 1. An object is moving only along the x-axis. Its velocity is given by 23()vt t t tαβ γ=+ + where α, β and γ are known constants. (Hint: 11,1nn n ndtnt tdt tdt n−==+∫.) (a) What is the object’s acceleration? (b) How far does it travel between the times 1t = sec and 2 sec?t = 2. (a) The equation of motion for an object is given by 32() ( )xtbtcte f=+− + where x is a position, t is the time, and b,c,e and f are constants. Obtain its velocity ()vt. (Hint: 1nndtntdt−=.) (b) The acceleration of an object which is moving along a straight line is given by 5() 3 4at t t=+ What is its position()xt? Assume that the object is initially(at 0)t=at rest at the origin, i.e. (0) 0x=.3. A person initially at point P in the illustration stays there for a moment and then moves along the axis to Q with velocity 1v and stays there for a moment. Then she runs quickly to R with velocity2v , stays there for a moment, and then strolls slowly back to P with velocity3v . (Therefore, 312vvv<<) 01234QRP Draw the position vs. time graph of this motion. 4. A football is punted with an initial velocity v0 at an angle of α above the horizontal on a long flat football field. Assume that the football leaves the punter’s foot at the ground level and calculate the following. (Hint: 0000() , ()ttttv v a t dt x x v t dt=+ =+∫∫) (a) The maximum height reached by the football. (b) The total time in the air before the ball hits the ground. (c) The total horizontal distance covered, i.e. the range. (d) The velocity of the football at the maximum height.position time5. (from Dr. Kamon’s class, Fall 2004) 6. In a uniform circular motion of a ball A, the centripetal acceleration is 2224AAAAAvRaRTπ== , where AR is the radius of the circular path, Av is the velocity of the ball A, and AT is its period. (a) What is the definition of the period T? (b) Another ball B is doing a uniform circular motion having the radius of RB =2RA. Assume that the centripetal acceleration of this ball is the same as the ball A. What is the velocity of the ball B? What is the period of the ball B? Write the answers in terms of the corresponding quantities of the ball
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