An automobile rolls down an incline, traveling $s(t) = 6t^2 + 3$ feet in $t$ seconds. What is the velocity at $t = 2$ , and after how many seconds will the velocity be $30$ $f$ $/$ $sec$ ?

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Answer 1 · 2015-12-04T16:20:29

$(a)$

$24"ft/s"$

$(b)$

$t=2.5"s"$

(a)

$s(t)=6t^2+3$

To find the velocity at a given instant we need to find the 1st derivative:

$s'(t)=v=12t$

So when $t=2$ :

$v=12xx2=24"ft/s"$

(b)

When $v=30$ :

$30=12xxt$

$:.t=30/12=2.5"s"$

An automobile rolls down an incline, traveling s(t) = 6t^2 + 3s(t) = 6t^2 + 3 feet in tt seconds. What is the velocity at t = 2t = 2, and after how many seconds will the velocity be 3030 ff//secsec?