A highway is to be constructed with a design speed of 100km/h. On one section of this highway, a +2.0% gradient of length 0.85km will be connected to a -1.5% gradient of length 1.20km. Estimate the power required for an electric vehicle of mass 2,000kg to travel from the start of the +2.0% gradient to the end of the section of road at the prescribed design speed. Take the coefficient of drag Co= 0.28, the frontal area of the vehicle At = 2.1m2 and air density p = 1.2256 kg/m3. Ignore the effects of vertical and horizontal curvature. [Recall Energy = Power x time) [5 marks] (b) ) With reference to Q2(a), an equal tangent vertical crest curve will be designed to connect the grades of +2.0% and -1.5%. Determine the length of curve required to meet the minimum stopping sight distance for a driver with eye height of 1.2m and an object of height 1.0m above the road surface. (Assume a perception-reaction time of 2.5 seconds and a coefficient of friction of 0.28). [5 marks] (c) Engineers wish to estimate the capacity of a road following the introduction of a specific autonomous vehicle technology that would replace human control in certain aspects of motorway driving. If the maximum deceleration of cars ranges from 6.2 m/s2 to 7.9 m/s2, and the length of cars ranges from 5.0m to 7.0m, considering the worst case scenario, estimate the safe following headway and hence the safe capacity of a single lane of motorway traffic with a design speed of 85km/h. Assume the response time of following autonomous vehicles is 0.1s and that the safety margin after an emergency stop is 1.0m. [5 marks] (d) The inside bend of a 2-lane single carriageway of width 7.2 metres has a horizontal radius of 750m and a superelevation of 2.5%. The road crosses a river, and the safety railings on the bridge are located 6.5 metres from the road's centre line. Calculate the maximum speed at which vehicles can safely negotiate this bend. Assume a perception-reaction time of 2 seconds, a coefficient of forward friction (1) (also known as the adhesion coefficient) of 0.3, and a coefficient of side friction (fs) or 0.15 [5 marks]