CPM Homework Help : CALC Problem 1-155

After Theo used the motion detector, he used his distance-time graph to determine the following properties of his motion. However, he has lost a copy of his graph. Help him re-create a possible graph of his motion.

DETAILS:

His average velocity was $0.5$ feet per second.
He turned around twice.
He started while standing $3$ feet from the motion detector and began to walk away from it at $t = 0$ .
He walked a total of $9$ feet during the $10$ -second interval.

Hint 1:

Clue 1: The slope from the first point to the last point should be $0.5$ , since that was the average velocity.

Hint 2:

Clue 2: The graph's slope should change its positivity/negativity twice, because Theo turned around twice.

Hint 3:

Clue 3: The first point should be $(0,3)$ because he started $3$ feet away from the motion detector.

Hint 4:

Clue 4: Your graph should consist of straight line segments, so that you can measure their length using the Pythagorean Theorem to make sure they total $9$ feet.