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 average velocity before t=0.4

Calculate average velocity between t=0.2 and t=0.4.
$\text{Average velocity} = \frac{s(0.4)-s(0.2)}{0.4-0.2} = \frac{1.5-0.5}{0.2} = 5$ ft/s

Step2: Find average velocity after t=0.4

Calculate average velocity between t=0.4 and t=0.6.
$\text{Average velocity} = \frac{s(0.6)-s(0.4)}{0.6-0.4} = \frac{3.8-1.5}{0.2} = 11.5$ ft/s

Step3: Average the two values

Estimate instantaneous velocity by averaging the two average velocities.
$\text{Estimated velocity} = \frac{5 + 11.5}{2} = 8.25$ ft/s

Answer:

8.25 feet per second