Question

practice it!
three people were jogging in the park. each person is represented as a, b, or c on
the distance-time graph.
select the statement(s) that accurately describe the data shown on the distance-
time graph.
person a traveled at a constant speed of 10 meters per second.
each person traveled at a constant speed.
person c traveled at a constant speed of 3 meters per second.
person b traveled at a slower speed than person a.
person b traveled the greatest distance.
graph: distance (m) vs time (s), y-axis 0–40, x-axis 0–6, with lines a, b, c, and a horizontal red line

Explanation:

To solve this, we analyze each statement using the distance - time graph (where speed = $\frac{\text{distance}}{\text{time}}$ for constant - speed motion, and a straight - line graph indicates constant speed):

Statement 1: Person A traveled at a constant speed of 10 meters per second.

• For Person A, at $t = 4$ seconds, the distance $d=40$ meters. Using the speed formula $v=\frac{d}{t}$, we get $v=\frac{40}{4}=10$ m/s. Also, the graph of Person A is a straight line, so the speed is constant. So this statement is correct.

Statement 2: Each person traveled at a constant speed.

• The graphs of A, B, and C are straight lines (Person C's graph is also a straight line, and Person B's graph is a straight line). A straight - line distance - time graph implies that the speed (slope of the line) is constant. So each person has a constant speed. This statement is correct.

Statement 3: Person C traveled at a constant speed of 3 meters per second.

• For Person C, at $t = 6$ seconds, the distance $d = 20$ meters. Using the speed formula $v=\frac{d}{t}$, we get $v=\frac{20}{6}\approx3.33$ m/s, not 3 m/s. So this statement is incorrect.

Statement 4: Person B traveled at a slower speed than Person A.

• For Person A, $v_A=\frac{40}{4} = 10$ m/s. For Person B, at $t = 6$ seconds, $d = 38$ meters (approx, from the graph). $v_B=\frac{38}{6}\approx6.33$ m/s. Since $6.33\lt10$, Person B's speed is slower than Person A's speed. This statement is correct.

Statement 5: Person B traveled the greatest distance.

• At $t = 6$ seconds, Person A would travel $d_A=10\times6 = 60$ meters (extrapolating from the speed), Person B would travel around 38 meters, and Person C would travel around 20 meters. So Person A travels the greatest distance, not Person B. This statement is incorrect.

Answer:

• Person A traveled at a constant speed of 10 meters per second. (Correct)
• Each person traveled at a constant speed. (Correct)
• Person B traveled at a slower speed than Person A. (Correct)