### Home > PC > Chapter 9 > Lesson 9.3.5 > Problem9-157

9-157.

Sketch the velocity function given by $v\left(t\right) = 6t$ for $0 ≤ t ≤ 5$.

1. Find the area under the curve from $t = 0$ to any value of $t$.

$\text{Area} = \frac{(\text{base})(\text{height})}{2}$

$\text{Area} = \frac{(t)(f(t))}{2}$

$\text{Area} = \frac{(t)(6t)}{2}$

Area $= 3t^{2}$

2. What does this area represent?

It represents distance traveled.