We will have the following:
First, we can see that the data presented is the following:
Now, from this information we can construct the following graphical relationship between time and distance drawn by the object:
From this we can infer that the relationship between time and distance is linear in nature, and the path of best descripton by linear regression is given by:
Where the approximation is:
[tex]f(x)=2.47204029x-0.4796893103[/tex]
We can see the linear relationship that fits the model, from this and the fact that in kinematics the following is true:
[tex]d=v\ast t[/tex]
Where "d" is the distace, "v" is the velocity and "t" the time.
From the data, the values of "x" represent the time and thus, the ratio of the function found is the velocity of the object.
In summary, the relationship is linear as per in kinematics, time and distace change proportionally in the data provided; and the approximated velocity of the object was 2.47m/s.
