Analyzing Graphs

Each of the graphs in Exercises 25 and 26 is the graph of the position function of an object moving on a coordinate line (t represents time). At approximately what times (if any) is each object’s (a) velocity equal to zero? (b) acceleration equal to zero? During approximately what time intervals does the object move (c) forward? (d) backward?

Solution Step 1of 4:

We have given a graph of the position function of an object moving on a coordinate line

(a)we have to determine at approximately what times is object's velocity equal to zero

From graph we have the critical point at which is

Hence at object's velocity equal to zero

Step 2 of 4:

(b)we have to determine at approximately what times is object's acceleration equal to zero

From the graph we can see that there is a points where the graph changes concavity and acceleration is equal to zero that is are