2. NO CALCULATOR IS ALLOWED FOR THIS QUESTION. Show all of your work. even though the question may not explicitly remind you to do 50. Clearly label any functions. gaphs. tables, or other objects that you use. Justications require that you give mathematical reasons. and that you verify the needed conditions under which relevant theorems. properties. defmitions. or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specied. answers (numeric or algebraic) need not be simplied. If yorn' answer is given as a decimal approximation. it should be correct to three places after the decimal point. Unless otherwise specied. the domain of a function f is assumed to be the set of all real numbers a: for which f (3:) is a real number. t29 312+8 ' A particle moves along the sic-axis so that its position at time t > 0 is given by 93(t) = (a) Show that the velocity of the particle at time t is given by v(t) : (MES-ts)" . (b) Is the particle moving toward the origin or away from the origin at time t = 2 '2 Give a reason for your answer. (c) The acceleration of the particle is given by a(t). Write an expression for a(t), and nd the value of (1(2). (d) What position does the particle approach as t approaches innity