Chapter 8.1, Problem 16E

To determine

To write approximately where does the particle achieve its greatest positive acceleration on the interval $\left[0,c\right]$

Answer to Problem 16E

The particle reaches its greatest positive acceleration approximately at point $t=c$ on the interval $\left[0,c\right]$

Explanation of Solution

Given information:

The figure shows the graph of velocity $v\left(t\right)$ .

Initial position of the particle at $t=0$ is $x\left(0\right)=15$ .the numbers shown in the graph are the areas of the enclosed region.

Acceleration is the rate of change of velocity with respect to time.

In the given interval $\left[0,c\right]$ velocity changes its sign at 0, a, b andc, but at point a and c only the velocity changes its sign from negative to positive. And the slope of velocity curve at point c is greater than that at point a.

Therefore,

The particle reaches its greatest positive acceleration approximately at point $t=c$.