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 $t$.

   Hint (a):

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

   Answer (a):

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

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

   Area $= 3t^{2}$

   

2. What does this area represent?

   Answer (b):

   It represents distance traveled.