Chapter 3.4, Problem 32E

To determine

To identify:the graph ofposition, velocity and acceleration.

Answer to Problem 32E

  $C$ is position function , $B$ is velocity function and $A$ is acceleration.

Explanation of Solution

Given information:

1. The graph of three functions is provided in figure 3.31 of the text book.
2. Need to identify which curve belongs to position function, velocity function and acceleration from $A$ , $B$ and $C$ .
3. Velocity function is first derivative of position function and acceleration is second derivative of position function.

First compare $C$ and $B$ . When $C$ is decreasing $B$ is negative. This means $B$ is derivative of $C$ .

Now compare $A$ and $B$ . When $B$ is decreasing $A$ is negative. When $B$ is minimum, $A$ is zero and when $B$ is increasing, $A$ is positive. This means $A$ is derivative of $B$ .

So on analysis we can say $C$ is position function whose first derivative $B$ is velocity function and first derivative of velocity function $B$ that is second derivative of position function $C$ is $A$ that is acceleration.