Question

the graph depicts the velocity and times of elan and anna during a race.
which best depicts the data?
○ from 0 to 2 seconds, anna experienced negative acceleration.
○ from 3 to 6 seconds, elan accelerated when anna did not.
● from 6 to 8 seconds, elan accelerated faster than anna.
○ from 8 to 10 seconds, elan experienced negative acceleration.

Explanation:

To determine the correct statement, we analyze the velocity - time graph. Acceleration is the slope of the velocity - time graph ($a=\frac{\Delta v}{\Delta t}$).

• For the option "From 0 to 2 seconds, Anna experienced negative acceleration": The slope of Anna's velocity - time graph from 0 to 2 seconds is positive (velocity is increasing), so acceleration is positive. This option is incorrect.
• For the option "From 3 to 6 seconds, Elan accelerated when Anna did not": From 3 to 6 seconds, Elan's velocity is constant (slope = 0, so acceleration = 0), and Anna's velocity is increasing (positive slope, so she is accelerating). So Elan is not accelerating while Anna is. This option is incorrect.
• For the option "From 6 to 8 seconds, Elan accelerated faster than Anna": The slope of Elan's velocity - time graph from 6 to 8 seconds is steeper than Anna's. Since acceleration is the slope of the velocity - time graph, a steeper slope means a larger acceleration. So Elan's acceleration is greater than Anna's in this time interval. This option is correct.
• For the option "From 8 to 10 seconds, Elan experienced negative acceleration": From 8 to 10 seconds, Elan's velocity is increasing (positive slope of the velocity - time graph), so acceleration is positive. This option is incorrect.

Answer:

From 6 to 8 seconds, Elan accelerated faster than Anna.