CPM Homework Help : APCALC Problem 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?

$734$ ft

$737$ ft

$747$ ft

$750$ ft

$752$ ft

Step 1:

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

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

Step 2:

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

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

Step 3:

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