Currently, the lost time of each stage is 4 seconds, and intersection critical v/c ratio is set to be 0.75 to avoid cycle failures caused by randomness of arrival traffic. Solve the following problems: 1) identify critical lane groups and solve their sum of flow ratios; 2) minimum cycle length and optimal cycle length; 3) Autonomous vehicle technologies make traffic movement at intersections more efficient. The lost time of each stage is reduced to 2 seconds, saturation headway is reduced by 10%. If the intersection demand does not change, calculate the critical v/c ratio corresponding to the minimum cycle length in 2).

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Afluid flows with a velocity field given by v=(x/t)i.. determine the local and convective accelerations when x=3 and t=1.

Shafts are machine elements that are used to a) carry axial loads b) direct shear loads c) transmit power d) rotate at constant speed e) none of the above circular and square shafts subjected to the same torque under the same circum behave a) the same way b) almost the same way