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Unformatted text preview: a z = d 2 z dt 2 = a = v z = dz dt = at and z = 1 2 at 2 Thus, the circumferential velocity is v = 4 3 at Now, we know that v = r d dt = d dt = 4 3 at R where we have used the fact that r = R . Integrating over time and imposing the initial condition (0) = 0 , we find = 2 3 at 2 R Therefore, the circumferential acceleration is a = r d 2 dt 2 + 2 dr dt d dt = 4 3 a Finally, since r = R , necessarily v r = dr/dt = 0 and a r = d 2 r dt 2 r w d dt W 2 = 16 9 a 2 t 2 R Therefore, the boys position, velocity and acceleration vectors are r = R w e r 1 2 at 2 R k W , v = at w 4 3 e k W , a = a w 16 9 at 2 R e r 4 3 e + k W...
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This note was uploaded on 10/12/2009 for the course AME 301 at USC.
 '06
 Shiflett

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