# 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?

Dec 4, 2015

$\left(a\right)$

$24 \text{ft/s}$

$\left(b\right)$

$t = 2.5 \text{s}$

#### Explanation:

(a)

$s \left(t\right) = 6 {t}^{2} + 3$

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

$s ' \left(t\right) = v = 12 t$

So when $t = 2$:

$v = 12 \times 2 = 24 \text{ft/s}$

(b)

When $v = 30$:

$30 = 12 \times t$

$\therefore t = \frac{30}{12} = 2.5 \text{s}$