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Little Casey Jones is getting an electric train set for Christmas. In the box, he finds 8 pieces of track ¾ four pieces of straight track, and four quarter-circle tracks. The straight tracks are 50 cm long, and the quarter circle tracks will form a circle of radius 50 cm if they are all put together. Casey assembles them into the figure shown at the right below. Casey sets the engine on the track and brings it up to a constant speed. The engine has a mass M and once it is up to speed, it takes 2 seconds to make one circuit of the track (at the speed Casey likes to use).

(a) Without actually calculating values, compare the instantaneous velocities of the train, (,,, and ) when it is at points B, C, and D.

 

(b) Calculate the average velocity of the train,, for the time interval it takes to go from point C to point D.

(c) Calculate the instantaneous acceleration, and , of the train when it is at points A and C.