Chapter 11.3, Problem 42E

Velocity    A car is moving along a straight test track. The position in feet of the car, s(t), at various times t is measured, with the following results.

t (sec)	0	2	4	6	8	10
s(t) (ft)	0	10	14	20	30	36

Find and interpret the average velocities for the following changes in t.

1. (a) 0 to 2 seconds
2. (b) 2 to 4 seconds
3. (c) 4 to 6 seconds
4. (d) 6 to 8 seconds
5. (e) Estimate the instantaneous velocity at 4 seconds
   1. (i) by finding the average velocity between 2 and 6 seconds, and
   2. (ii) by averaging the answers for the average velocity in the two seconds before and the two seconds after (that is, the answers to parts (b) and (c)).
6. (f) Estimate the instantaneous velocity at 6 seconds using the two methods in part (e).
7. (g) Notice in parts (e) and (f) that your two answers are the same. Discuss whether this will always be the case, and why or why not.