Question

How does the velocity of a falling object change with time? How would you describe the mathematical relationship between velocity and time of a falling object? Explain the answer using your data, graphs, and the kinematic equations.The image below shows the ball stopping at 2 4 6 8 and 10 and how long it took it too stop there

Answer 1

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:

`f(x)=2.47204029x-0.4796893103`

We can see the linear relationship that fits the model, from this and the fact that in kinematics the following is true:

`d=v\ast t`

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.