Chapter 5, Problem 66RE

The velocity of a particle moving along an s-axis is measured at $5\text{ s}$ intervals for $40\text{ s}$

, and the velocity function is modeled by a smooth curve. (The curve and the data points are shown in the accompanying figure.) Use this model in each part.

(a) Does the particle have constant acceleration? Explain your reasoning.

(b) Is there any $15\text{ s}$ time interval during which the acceleration is constant? Explain your reasoning.

(c) Estimate the distance traveled by the particle from time $t=0$ to time $t=40$ .

(d) Estimate the average velocity of the particle over the $40\text{ s}$

time period.

(e) Is the particle ever slowing down during the $40\text{ s}$ time period? Explain your reasoning.

(f) Is there sufficient information for you to determine the s-coordinate of the particle at time $t=10$ ? If so, find it. If not, explain what additional information you need.