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AP® Calculus AB-BC

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Moderate

Total Distance Of A Particle

APCALC-LYHI08

A particle in the $xy$-plane moves according to the following equations: $x(t)=\cfrac {1}{2} \cdot t^2+t + 4$ and $y(t)=\cfrac {3}{2} \cdot t^2-2t -8.$

Find the correct expression for the total distance the particle has traveled from time $t = 1$ to $5$.

A

$\int _{ 1 }^{ 5 }{ \sqrt { { 10t }^{ 2 }-10t+5 } \,dt } $

B

$\int _{ 1 }^{ 5 }{ \sqrt { { -10t }^{ 2 }+10t-5 } \,dt } $

C

$\int _{ 1 }^{ 5 }{ \sqrt { { 16t }^{ 2 }-8t+1 } \,dt } $

D

$\int _{ 1 }^{ 5 }{ \sqrt { 4t-1 } \,dt } $