1. A particle moves with velocity v(t) = (3t, t2, te') for 0 < t < 2 and is initially at the origin (0,0,0) (at time t = 0). (a) Find the particle's position function r(t). (b) Find the particle's acceleration function a(t). (c) Find the work done on the particle by a force F that points directly in the vertical k-direction with magnitude eve at each point (x, y, z).

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