Question

current attempt in progress
the position s of a car at time t is given in the following table.

t (sec)	0	0.2	0.4	0.6	0.8	1.0
s (ft)	0	0.3	1.6	4.0	6.6	9.4

(a) find the average velocity over the interval 0 ≤ t ≤ 0.2.
enter the exact answer.
the average velocity over the interval 0 ≤ t ≤ 0.2 is
ft/sec.
(b) find the average velocity over the interval 0.2 ≤ t ≤ 0.4.
enter the exact answer.
the average velocity over the interval 0.2 ≤ t ≤ 0.4 is
ft/sec.
(c) use the previous answers to estimate the instantaneous velocity of the car at t = 0.2.
enter the exact answer.
the instantaneous velocity at t = 0.2 is
ft/sec.
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Explanation:

Step1: Recall average - velocity formula

The average velocity $v_{avg}$ over the interval $[a,b]$ is given by $v_{avg}=\frac{s(b)-s(a)}{b - a}$, where $s(t)$ is the position - function and $t$ is time.

Step2: Calculate average velocity for $0\leq t\leq0.2$

For the interval $0\leq t\leq0.2$, $a = 0$, $b = 0.2$, $s(0)=0$, and $s(0.2)=0.3$. Then $v_{avg}=\frac{s(0.2)-s(0)}{0.2 - 0}=\frac{0.3-0}{0.2}=\frac{0.3}{0.2}=1.5$ ft/sec.

Step3: Calculate average velocity for $0.2\leq t\leq0.4$

For the interval $0.2\leq t\leq0.4$, $a = 0.2$, $b = 0.4$, $s(0.2)=0.3$, and $s(0.4)=1.6$. Then $v_{avg}=\frac{s(0.4)-s(0.2)}{0.4 - 0.2}=\frac{1.6 - 0.3}{0.2}=\frac{1.3}{0.2}=6.5$ ft/sec.

Step4: Estimate instantaneous velocity at $t = 0.2$

The instantaneous velocity at $t = 0.2$ can be estimated as the average of the average velocities on the intervals $[0,0.2]$ and $[0.2,0.4]$. So $v(0.2)\approx\frac{1.5 + 6.5}{2}=\frac{8}{2}=4$ ft/sec.

Answer:

(a) 1.5 ft/sec
(b) 6.5 ft/sec
(c) 4 ft/sec