Mathematics

Mathematics

Problem

For 0≤t≤20\le t\le 2, curve PP has speed vP(t)=4+t2v_P(t)=\sqrt{4+t^{2}} and curve QQ has speed vQ(t)=t+2v_Q(t)=t+2. Which of the following is true about their arc lengths over this interval? a) Length(P)>Length(Q)\text{Length}(P) > \text{Length}(Q) b) Insufficient information to compare the two arc lengths c) Length(P)<Length(Q)\text{Length}(P) < \text{Length}(Q) d) Length(P)=Length(Q)\text{Length}(P) = \text{Length}(Q)

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