The velocity of a roller coaster car in meters per second on a certain segment of track is represented by the function $v(t) = -8t$.

1. Sketch a graph of the velocity function for $0\le t\le4$. What is the speed of the car at $t = 4$?

   Hint (a):

   Recall that speed is the absolute value of velocity.

   Answer (a):

   $\left| v(4) \right| = \left|− 32 \right| = 32$
   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 (b):

   $\text{final position} = \text{initial position} + \text{displacement}$

   Hint (b):

   initial position is $100$ meters

   Hint (b):

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

   Hint (b):

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