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2. (a) A particle P moves along the x-axis with constant acceleration a in the positive x-direction. Initially P is at the origin and is moving with velocity u in the positive x-direction. Show that the velocity v and displacement x of P at time t are given by v = u + at, x = ut + 1 2 at2 , and deduce that v 2 = u 2 + 2ax. (b) The trajectory of a charged particle moving in a magnetic field is given by r = b cos (Ωt)i + b sin (Ωt)j + ctk, where b, Ω and c are positive constants. Show that the particle moves with constant speed and find the magnitude of its acceleration.
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