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

1-37.

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?

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.

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 $0 ≤ x ≤ 2$.

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