Question

the graph depicts the velocity and times of elan and anna during a race. which best describes the data? from 0 to 2 seconds, anna experienced negative acceleration. from 2 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.

Explanation:

To solve this, we analyze each option by interpreting the velocity - time graph (slope represents acceleration, horizontal line means constant velocity (zero acceleration), steeper slope means greater acceleration):

Analyzing Option 1: From 0 to 2 seconds, Aena experienced negative acceleration.

The slope of Aena's graph from 0 to 2 seconds is positive (since the velocity is increasing with time). So, Aena has positive acceleration, not negative. This option is incorrect.

Analyzing Option 2: From 2 to 6 seconds, Elan's velocity was constant.

Elan's graph from 2 to 6 seconds is a horizontal line. In a velocity - time graph, a horizontal line indicates that the velocity is constant (because the change in velocity $\Delta v = 0$ over that time interval). So, Elan's velocity was constant during this time. This option is correct.

Analyzing Option 3: From 6 to 8 seconds, Elan accelerated faster than Aena.

The slope of Elan's graph from 6 to 8 seconds is steeper than Aena's slope. The slope of a velocity - time graph represents acceleration ($a=\frac{\Delta v}{\Delta t}$). A steeper slope means a greater change in velocity over the same time interval, so Elan's acceleration is greater than Aena's? Wait, no, wait. Wait, the problem says "Elan accelerated faster than Aena". But let's re - check. Wait, in the graph, from 6 to 8 seconds, Elan's velocity - time graph has a steeper slope. But wait, maybe I misread. Wait, no, the third option says "From 6 to 8 seconds, Elan accelerated faster than Aena". But let's check the first correct option. Wait, the second option: "From 2 to 6 seconds, Elan's velocity was constant." In a velocity - time graph, a horizontal line means constant velocity (acceleration $a = 0$). So this is a correct statement.

Analyzing Option 4: From 8 to 10 seconds, Elan experienced negative acceleration.

The slope of Elan's graph from 8 to 10 seconds is positive (velocity is increasing), so acceleration is positive, not negative. This option is incorrect.

Answer:

B. From 2 to 6 seconds, Elan's velocity was constant.