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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2.7, Problem 48E

(a)

To determine

**To find:** The acceleration at

Expert Solution

At ^{-2}.

The graph of the position function is given with *s* in feet and *t* in seconds.

From the given graph, it is observed that the slope of the position function is always positive for

The slope of the curve increases very slowly initially, then just before

The slope of the curve increases very rapidly and then the increase in slope decreases just after

After the time just before

**Graph:**

Use the above information and trace the graph of velocity function as shown below in Figure 1.

From Figure 1, it is observed that velocity contains the horizontal tangent at one point.

Let the point be *A*.

Note that, the value of the derivative will be zero at the point where the function has the horizontal tangent.

Thus, the graph of acceleration will be zero at the points *A*.

At

At

Use the above information and trace the graph of acceleration function as shown below in Figure 2.

From Figure 2, it is observed that the acceleration is positive in the first half and negative in the second half.

From the Figure 2, at ^{-2}.

**(b)**

To determine

**To calculate:** The jerk at

Expert Solution

The jerk at ^{-3}.

**Estimation:**

Draw the tangent at

**Calculation:**

The jerk at

From the Figure 3, take two points in the vicinity of

Let these two point be *A* and *B*.

Slope of the curve at *A* to *B*.

Thus,

Therefore, the jerk at ^{-3}.