1. You are going to Taichung for the weekend and decide to go first-class by taking...

Transcribed Image Text:

1. You are going to Taichung for the weekend and decide to go first-class by taking the High-Speed Rail train. Unfortunately, you finished your mathematics exam late and arrived at the train station late. You run as fast as you can, but just as you reach the platform, your train departs, 30 meters ahead of you down the platform. The train is accelerating at 0.8 m/s. You can run along the platform for 40 meters before a barrier prevents you from going further. (a) What minimum speed do you need to run to just catch up with the train? (Let's assume the door of the train is open :D) (b) how much time do you have to run to catch the train? (c) how fast is the train traveling when you catch it? (35 points) 2. As a weather balloon ascends at constant speed, one of its instrument packages breaks free of a harness and free-falls. Figure 1 gives the vertical velocity of the package versus time, from before it breaks free to when it reaches the ground. (a) What maximum height above the break-free point does it rise? (b) How high is the break-free point above the ground? (30 points) 3. V 0 t(s) 4 Figure 1 An object's velocity is measured to be u (t) = - t, where = 4.00 m/s and =2.00 m/s. At t = 0 the object is at x = 0. (a) Calculate the object's position and acceleration as functions of time. (b) What is the object's maximum positive displacement from the origin? (35 points) 1. You are going to Taichung for the weekend and decide to go first-class by taking the High-Speed Rail train. Unfortunately, you finished your mathematics exam late and arrived at the train station late. You run as fast as you can, but just as you reach the platform, your train departs, 30 meters ahead of you down the platform. The train is accelerating at 0.8 m/s. You can run along the platform for 40 meters before a barrier prevents you from going further. (a) What minimum speed do you need to run to just catch up with the train? (Let's assume the door of the train is open :D) (b) how much time do you have to run to catch the train? (c) how fast is the train traveling when you catch it? (35 points) 2. As a weather balloon ascends at constant speed, one of its instrument packages breaks free of a harness and free-falls. Figure 1 gives the vertical velocity of the package versus time, from before it breaks free to when it reaches the ground. (a) What maximum height above the break-free point does it rise? (b) How high is the break-free point above the ground? (30 points) 3. V 0 t(s) 4 Figure 1 An object's velocity is measured to be u (t) = - t, where = 4.00 m/s and =2.00 m/s. At t = 0 the object is at x = 0. (a) Calculate the object's position and acceleration as functions of time. (b) What is the object's maximum positive displacement from the origin? (35 points)