### Home > CALC > Chapter 3 > Lesson 3.3.4 > Problem 3-139

3-139.

While riding a roller coaster, the velocity in meters per second on a certain segment of track is represented by the function

*v*(*t*) = −8*t*. Homework Help ✎Sketch a graph of

*v*(*t*) for 0 ≤*t*≤ 4. What is the speed of the car at*t*= 4?Assuming that the car is 100 meters above ground at

*t*= 0, where is the car at*t*= 4? How far is this drop?

Recall that speed is the absolute value of velocity.

|*v*(4)| = |− 32| = 32

Don't forget the units!

final position = initial position + displacement

intial position is 100 meters

Displacement is area between the velocity curve and *x*-axis. Notice that the area is negative (below the *x*-axis).

Total distance of the drop = area under a SPEED graph.