You are sitting on your bike at rest. Your brother comes running at you from behind at a speed of 2 m/s. At the exact moment he passes you, you start up on your bike with an acceleration of 2m/s2. 1. Draw a picture of the situation, defining the starting positions, speeds, etc.
2. At what time t do you have the same speed as your brother?
3. At what time t do you pass your brother?
4. Draw another picture of the exact moment you catch your brother. Label the drawing with the positions and speeds at that moment.
5. Sketch a position vs. time graph for both you and your brother, labeling the important points (i. e., starting point, when you catch him, etc.)
6. Sketch a speed vs. time graph for both you and your brother, labeling the important points (i. e., starting point, when you catch him, etc.)

Find the steady-state temperature at the center of the plate = /2, = /2) for sums of w from n=1 to n=19 (only odd values). find the value of n for which the change in /2, /2) is less than 1% from the value at the previous n. at this point, we consider the solution converged. does the value of the temperature at the center seem reasonable? in this part, the values of x and y are constant scalar values. you should produce a plot of the value of n on the horizontal and the estimate of the temperature at the center of the plate on the vertical. b. using the value of n (or larger) that resulted in convergence in part (a), create a contourf plot of the temperature distribution across the entire plate. use enough spatial subdivisions to create a useful plot. comment on the results. hint: you need to determine what “x” and “y” values to use to make your t matrix. i recommend using a different number of x and y values. use enough x and y values so that the plot is “smooth”.