I1 Motion with Constant Velocity In this assignment, we will explore graphs in the case of motion with constant velocity. Many ideas from this exploration will be important when we discuss motion with constant acceleration in class. As a reminder, here are the equations of motion for a physical system that moves with constant velocity. We assume that everything happens in one dimension: xm =2m+a (1) v = 0111an [2) where x[t) is the position at a time t, x0 is the initial position at the initial time to [usually considered to be to: 0]. v is [the corresponding component of) the velocity. 1. Anh-Thu walks from PCL to the PMA building following a path that can be very well described by a straight line. When she checks her smartwatch, she sees that she walked at an average speed of 3 miles per hour. We will consider the direction in which she travelled as positive. Write your answers using meters and seconds. [a] (5%] If Anh-Thu walked for 8 minutes, what is her displacement Ax in meters? (b) [5%] Consider the starting point to be the origin, Lxo = 0 m. Write the position x[t] [in meters) as a function of time t [in seconds). [c] (5%] Draw the position vs. time graph for Anh-Thu's 8-minute walk. Remember that the dependent variable > vertical axis and independent variable > horizontal axis. (d) (5%] Calculate the slope of the linear function. What is its relation to Anh-Thu's velocity? (e) [5%] Draw the velocity vs. time graph. [1] (5%] Use the velocity vs. time graph to calculate the area between the velocity line and the horizontal axis. Compare the value and unit of this area with Anh-Thu's displacement. Is there any relation that you observe between these two quantities? 2. Once physics class is over, AnhThu leaves the PMA building to go work out at Greg gym. It takes her about 3 minutes to run 0.3 miles to get there, travelling in what we consider to be the negative direction. Use meters and seconds for your answers. (a) [5%) What is AnhThu's velocity Vin m/s? Make sure to use the correct sign. [b] [5%) What is AnhThu's displacement Ax in meters? Make sure to use the correct sign. (c) [5%) Consider the starting point to be x0 = 0.3 miles. Write the position x[t) [in meters) as a function oftime t [in seconds). [d] [5%) Draw the position vs. time graph for Anh-Thu's 3-minute run. Remember that the dependent variable > vertical axis and independent variable ' horizontal axis. (e) [5%) Calculate the slope of the linear function. What is its relation to Anh-Thu's velocity? [0 [5%) Draw the velocity vs. time graph. [g] [5%) Use the velocity vs. time graph to calculate the area between the velocity line and the horizontal axis. Compare the value and unit of this area with Anh-Thu's displacement. Is there any relation that you observe between these two quantities? [In this case, you should get a negative area. Weird, huh?) 3. [8%] For the graph below, calculate the area between the velocity curve and the horizontal axis. Write the area in terms of the quantities gancl v. Mauls W63 {f Time, (5) 4. [9%] What is the relationship between the area you calculated in the previous part and the displacement Ax? Justify and explain your answer. 5. [9%] For the graph below, calculate the slope of the position curve. Write the slope in terms of the quantities to, g; xaandg Qosx'dom (\"'\\ - 5 Ti '60 if M (S) 6. [9%] What is the relationship between the slope that you calculated in the previous part and the velocity v? Justify and explain your