A path is traced in two consecutive time intervals

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

A path is traced in two consecutive time intervals. Segment 1 ( 0≤t≤10\le t\le 1 ): r1(t)=⟨3t, 4t⟩\mathbf r_1(t)=\langle 3t,\,4t\rangle Segment 2 ( 1<t≤21< t\le 2 ): r2(t)=⟨3+(t−1)2, 4+2(t−1)⟩\mathbf r_2(t)=\langle 3+(t-1)^2,\,4+2(t-1)\rangle Compute the total length of the entire path from t=0t=0 to t=2t=2.

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