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Total solidification times of three casting geometries are to be compared: a sphere, a cylinder, in which the length-to-diameter ration - 1.0, and a cube. volume = 1000 cm^3 for all three shhapes, and the same casting alloy is used. a) determine the solidification times of each geometry b) based on the results of part (a), which geometric element would make the best riser? c) if the mold constant = 3.5 min/cm^2 in chvorinov's rule, compute the total solidification time for each casting.

Given the position vector of the particle r(t)=(t+1)i+(t^2−1)j+2t k, find the particle's velocity and acceleration vectors at t=1

If the force applied to an object remains constant, is more power needed for the object to move faster ? explain