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

1. Sketch a graph of $v(t)$ for $0 ≤ t ≤ 4$. What is the speed of the car at $t = 4$?

   Hint (a):

   Recall that speed is the absolute value of velocity.

   Answer (a):

   $|v(4)| = |− 32| = 32$
   Don't forget the units!

2. Assuming that the car is $100$ meters above ground at $t = 0$, where is the car at $t = 4$? How far is this drop?

   Hint 1(b):

   final position $=$ initial position $+$ displacement

   Hint 2(b):

   initial position is $100$ meters

   Hint 3(b):

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

   Hint 4(b):

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