A car travels at a rate of $v(t) = 20t + 30$ miles per hour for $0 ≤ t ≤ T$.

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

2. Shade the area under the curve for $0 ≤ t ≤ T$. 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.

   The two bases represent velocity in (mph). The height of the trapezoid is time, in hours.

   Evaluate the area of the trapezoid simplifying the units.

4. Compute the area under the curve for $0 ≤ t ≤ 2$. What does your answer represent?

   Hint (d):

   Find $A (20x + 30, 0 ≤ x ≤ 2)$.