Question

The graph depicts the velocity and times of Elan and Anna during a race.

A graph with horizontal axis time (seconds) and vertical axis velocity (meters per second). A green line labeled Anna runs in straight segments from 0 seconds 0 meters per second to 1 second 6 meters per second to 10 seconds 24 meters per second. A red line labeled Elan runs in straight segments from 0 seconds 0 meters for second to 1 second 1 meter per second to 3 seconds 10 meters per second to 6 seconds 10 meters per second to 8 seconds 20 meters per second to 10 seconds 25 meters per second.

Which best depicts the data?

From 0 to 2 seconds, Anna experienced negative acceleration.
From 3 to 6 seconds, Elan accelerated while Anna did not.
From 6 to 8 seconds, Elan accelerated faster than Anna.
From 8 to 10 seconds, Elan experienced negative acceleration.

Answer 1

Only the third statement is correct.

Reasoning (acceleration = slope of v vs t):
- Anna: 0–1 s: a = (6−0)/1 = 6 m/s²; 1–10 s: a = (24−6)/9 = 2 m/s². So Anna never has negative acceleration.
- Statement 1 is false.
- Elan: 0–1 s: a = 1 m/s²; 1–3 s: a = (10−1)/2 = 4.5 m/s²; 3–6 s: a = 0; 6–8 s: a = (20−10)/2 = 5 m/s²; 8–10 s: a = (25−20)/2 = 2.5 m/s².
- Statement 2 is false (Elan does not accelerate 3–6 s; Anna does).
- Statement 3 is true (5 > 2).
- Statement 4 is false (Elan’s acceleration 8–10 s is +2.5 m/s², not negative).