FI ITCM Section Two (al mark) (please answer in a fresh booklet) A particle moves on a smooth horizontal surface with acceleration (31 - 5j) ms". Initially the velocity of the particle is 4j ms . (a) Find an expression for the velocity of the particle at time t seconds. (b) Find the time when the particle is travelling in the i direction. [2) (c) Show that when t = 4 the speed of the particle is 20 ms-. 7. Two particles, A of mass 5 kg and B of mass 9 kg, are attached to the ends of a light inextensible string. The string passes over a light smooth pulley as shown in the diagram. The particles are released from rest at the same height. A OB (a) By forming an equation of motion for each particle, show that the magnitude of the acceleration of each particle is 2.8 ms 2. [4] (b) Find the tension in the string. (2] (c) When B has been moving for 0.5 seconds it hits the floor. Find the height of A, above the floor, at this time. Assume that A is still below the pulley when B hits the floor. [4] TURN OVER for17CM 3. The table below shows the numbers of males and females in each of three employment categories at a university on 31 July 2003. Employment category Managerial Academic Support Male 38 369 303 Female 26 275 643 (a) An employee is selected at random. Determine the probability that the employee is: i. female; (1] ii. a female academic; [1] ili. either female or academic or both; 12] iv, female, given that the employee is academic. [2] (b) Three employees are selected at random, without replacement. Determine the probability that i. all three employees are male; [2] ii. exactly one employee is male. [3] (c) The event "employee selected is academic" is denoted by A. The event "employee selected is female" is denoted by F. Describe in context, as simply as possible, the events denoted by: i. FoA; ii. FUA. [1 TURN OVER for