### Home > CALC > Chapter 1 > Lesson 1.2.2 > Problem1-37

1-37.
1. A car travels at a rate of 20x + 30 miles per hour for 0 ≤ xt. 1-37 HW eTool (Desmos) Homework Help ✎

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

2. Shade the area under the curve for 0 ≤ xt. What does this area represent?

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

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

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

The shape is a trapezoid.

$\text{base_1 and base_2 are vertical, so they represent velocity \left(in\ \frac{miles}{hour}\right).}$

Height is horizontal, so it represents time, in hours. Evaluate the area of a trapezoid. Simplify the units.

Find A (20x + 30, 0 ≤ x ≤ 2).

Use the eTool below to set values for t.
Click the link at right for the full version of the eTool: Calc 1-37 HW eTool