Not quite sure what format you mean, but this should help... r(t)=( t², ( t+t³)/3, (t-t³)/3 ) v(t) = dr/dt . . .
. = ( 2t, (1+2t²)/3, (1-2t²)/3 ) When t=0 this is: v(0) =( 2(0), (1+2(0)²)/3, (1-2(0)²)/3 ) . .
. . = ( 0, 1/3, 1/3 ) Note ||v(0)|| may be needed later, so I'll work it out now: v(0)|| =?(0² + (1/3)² + (1/3)² ) .
. . .
. . =?(2/9) .
. . .
. . =?2/3 a(t) = dv/dt .
. . .
= ( 2, (4/3)t, -(4/3)t ) When t=0 this is: a(0) = (2, (4/3)0, -(4/3)0 ) . . .
. = (2, 0, 0) There are various formulae to find the tangential and normal components. I would use.
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