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 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

Explanation :

The given graph depicts the velocity-time graph for both Elan and Anna during a race.

In this velocity-time graph, it shows the acceleration of Elan and Anna for different time intervals.

We know that acceleration is defined as :

`a = (v-u)/(t)`

Where,

v is the final velocity

u is the initial velocity

and t is the time taken

We know that the slope of the v - t graph gives the acceleration of an object.

So, it can be seen that from 6 to 8 seconds, Elan accelerated faster than Anna as the slope for Elan is more.

So, the correct option is (c) " From 6 to 8 seconds, Elan accelerated faster than Anna ".

Answer 2

For this case, the first thing you should observe is the variables:

Vertical axis: speed

Horizontal axis: time

Since the relationship between both variables is linear then we have that the slope of the line represents the acceleration according to the formula:

`image`

Where,

a: acceleration

t: time

vf: final speed

vo: initial speed

According to the equation, in the interval of 6 to 8 seconds, we observe that the slope of the Elan line is greater than the slope of the Anna line.

Therefore, for the 6 to 8 second interval, the Elan acceleration is greater.

Answer:

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