### Home > APCALC > Chapter 11 > Lesson 11.1.3 > Problem11-38

11-38.

Multiple Choice: A racer with a $5$-foot head start runs with an acceleration of $a(t) = 6t \text{ ft} / \sec^2$. At $t = 4$ seconds, her velocity is $50$ ft/sec and she finishes the race in $9$ seconds. How long was the race? Homework Help ✎

1. $734$ ft

1. $737$ ft

1. $747$ ft

1. $750$ ft

1. $752$ ft

$v(t)=\int 6tdt=3t^2+C$

Use $v\left(4\right) = 50$ to solve for $C$.

$d(t)=\int(3t^2+2)dt=t^3+2t+C$

Use $d\left(0\right) = 5$ to solve for C.

Use your equation for $d\left(t\right)$ to evaluate $d\left(9\right)$.