A train accelerates along a straight, horizontal section of track. The driver notes that he reaches a bridge Com from the station in 8 s and that he crosses the bridge, which is 31.Sm long, in a further 2 s. The motion of The train is modelled by assuming constant acceleration. Take the speed of the train when leaving the station to be ums" and the acceleration to have the value ams? ) By considering the part of the journey from the station to the bridge, show that u + 4a = 15 (ii) Find a second equation involving u and a. (iii) Solve the two equations for u and a to show that a is 0.15 and find the value of u. (iv) If the driver also notes that he travels 167m in the 10 s after he crosses the bridge, have you any evidence to reject the modelling assumption that the acceleration is constant? [ 1 1. The diagram shows the velocity-time graph for a lift moving between floors in a building. The graph consists of straight line segments. In the first stage the lift travels downwards from the ground floor for 5 s, coming to rest at the basement after travelling 10m. The second stage consists of a 10 s wait at the basement. In the third stage, the lift travels upwards until it comes to rest at a floor 34.5m above the basement, arriving 24.5 s after the start of the first stage. The lift accelerates at 2ms 2 for the first 3 s of the third stage, reaching a speed of Vms . Find ii) the value of V, (iii) the time during the third stage for which the lift is moving at constant speed, (iv) the deceleration of the lift in the final part of the third stage. 12. A particle is projected vertically upwards from a point O with initial speed 12.5ms . At the same instant another particle is released from rest at a point 10m vertically above O. Find the height above O at which the particles meet