A car travels at a rate of $20x + 30$ miles per hour for $0 ≤ x ≤ t$.

1. Sketch a velocity graph and label the axes with the correct units.

2. Shade the area under the curve for $0 ≤ x ≤ t$. What does this area represent?

   Hint (b):

   The area represents distance traveled (or displacement) between $x = 0$ and $x = t$.

3. What are the units of the area? Explain how you know.

   Hint (c):

   The shape is a trapezoid.
   base $1$ and base $2$ are vertical, so they represent velocity $\frac{\text{miles}}{\text{hour}}$
   Height is horizontal, so it represents time, in hours. Evaluate the area of a trapezoid. Simplify the units.

4. Compute the distance traveled for $0 ≤ x ≤ 2$.

   Hint (d):

   Find $A(20x + 30,$ $0 ≤ x ≤ 2)$.