For , curve has speed and curve has speed . Which of the following is true about…

MATHEMATICS · Single correct · AP · Calculus BC · Applications of Integration · Applications of Integration

Problem

For

0\le t\le 2

, curve

P

has speed

v_P(t)=\sqrt{4+t^{2}}

and curve

Q

has speed

v_Q(t)=t+2

. Which of the following is true about their arc lengths over this interval? (a)

\text{Length}(P) > \text{Length}(Q)

(b) Insufficient information to compare the two arc lengths (c)

\text{Length}(P) < \text{Length}(Q)

(d)

\text{Length}(P) = \text{Length}(Q)