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. This is the velocity time and graph

Answer 1

We have the following obervations:

Where v is obtaineg by dividing the distance by the time. Now, if we plot the time and the velocity on the plane we will get the following graph:

From the graph we notice that:

• As time increases the velocity of the object increases as well.

,

• It appears that we can model this increase in the velocity with a linear equation on the time, in the graph shown above we notice that if we perform a linear regression we get the equation:

`v=0.0432t+1.1206`

and that the line is a good fit. Now, the equation we got has the form:

`v=at+v_0`

where a is the acceleration of the ball and v0 is its initial velocity.

Now, even the line we obtain is a good fit for the data we found we know that something is wrong. This comes from the fact that the initial velocity of the object is 1.12 for the line we found and we know that, in our experiment, the initial velocity is zero. This would mean that we need to perform the experiment a few more times to correctly measure what is happening.

Even from this, we are certain of two things that we mention above:

• As time increases the velocity of the object increases as well.

,

• The velocity of the object as it is falling in the ramp can be modeled by a linear equation.