Question

1. (5pts) a car’s position, s, measured in feet, after t seconds is given by the table:

t	0	0.2	0.4	0.6
s	0	0.5	1.5	3.8

estimate the instantaneous velocity at t = 0.4.

Explanation:

Step1: Find left average velocity

Calculate average velocity from $t=0.2$ to $t=0.4$:
$\frac{s(0.4)-s(0.2)}{0.4-0.2} = \frac{1.5-0.5}{0.2} = 5$ ft/s

Step2: Find right average velocity

Calculate average velocity from $t=0.4$ to $t=0.6$:
$\frac{s(0.6)-s(0.4)}{0.6-0.4} = \frac{3.8-1.5}{0.2} = 11.5$ ft/s

Step3: Average the two values

Estimate instantaneous velocity by averaging left and right velocities:
$\frac{5 + 11.5}{2}$

Answer:

8.25 feet per second