While riding a roller coaster, the velocity in meters per second on a certain segment of track is represented by the function v(t) = −8t. 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.