Question

A small package is released from rest at A and moves along the skate wheel conveyor ABCD. The package has a uniform acceleration of 6.2 m/s2 as it moves down sections AB and CD, and its velocity is constant between B and C. The velocity of the package at D is 7.2 m/s. a) Determine the distance d between C and D. (Round the final answer to two decimal places.) in m. b) the time required for the package to reach D. in s.

Answer 1

a_AB = a_CD = 6.2 m/s^2 v_1 = v_BC = constant = > a_BC = 0 V_D = 7.2 m/s Along AB v = u + at_1 v_1 = 0 + 6.2 times t_1 v_1 = 6.2 t_1 S = 1/2 times 6.2 t^2_1 S_1 = 3.1 t^2_1 Along BC V = u i.e v = v_1 s = ut_2 + 1/2 at^2_2 S_2 = v_1t_2 + 1/2 (0) t^2_2 s_2 = v_1 t_2 along CD v_D = v_1 + at_3 7.2 = v_1 + 6.2 t_3 s_3 = v_1t_3 + 1/2 at^2_3 d = v_1t_3 + 1/2 at^2_3 d = v_1t_3 + 3.1 t^2_3 \r\n assuming t_1 = t_2 = t_3 = t Therefore d = v_1t + 3.1 t^2 from equation (1) v_1 = 6.2 t and equation (4) 7.2 = v_1 + 6.2 t = > 7.2 = v_1 + v_1 v_1 = 7.2/2 = 3.1 m/s Therefore t = v_1/6.2