Understanding the Free Fall Velocity Equation

[RJLiberator]

Homework Statement

I am tasked with coding some graphs regarding free fall motion.

I am unclear what the professor means regarding the following, so I am looking for incite here.

Problem: Solve numerically free fall velocity equation (problem 1.1), compare with exact solution
(1.1) dv/dt = -g

The exact numerical solution and the coding solution should agree here.

My problem is what does dv/dt= -g mean as free fall velocity?

I thought that when you take the derivative of velocity, you get acceleration. That should be what it is saying. (as it is).
She states that she wants us to solve the free fall velocity equation and directs us to dv/dt=-g. Does this make sense?

My understanding is that free fall velocity is v(t) = g*t which is a linear graph Any clarity on the wording?
note* I can't talk to her as it is due Monday.

 

[haruspex]

V=-gt would be the exact solution, assuming zero velocity at time 0. A numerical solution would consist of calculating the velocity at a sequence of times using the relationship $\Delta v=(dv/dt)\Delta t$. You are given what to substitute for dv/dt.

 

[RJLiberator]

Okay, so we both agree that this graph should be linear and that what she is asking for the a velocity graph.
The exact solution I was able to graph and I took into account initial velocity.

So now I have to just add in the numerical solution as you stated.
The numerical solution would then be -g*(change in time)
But this doesn't make sense to me. Because -g*change in time would just be a constant and not a linear down slope.

 

[haruspex]

But this doesn't make sense to me. Because -g*change in time would just be a constant and not a linear down slope.

Change in velocity = -g*change in time . Pick some time interval $\Delta t=T$.
v₀=0;
v₁=v₀+(-g)T;
etc.

 

[RJLiberator]

Ah, beautiful.

I just want to confirm one thing with you.
The assignment calls for:
–Solve numerically free fall velocity equation (problem 1.1), compare with exact solution
and later states:
Use TGraph to show numerical solution for v(t) and TF1 to illustrate the exact solution (on top of it)

For some reason, she drew a slightly parabolic curve for the 'example graph' in class on the white board.
I don't see how this could, in any sense, be parabolic and I don't understand how any of our current analysis could be skewed.

We seem to be right on with what she has stated as the assignment here and I will use my exact solution (previously pictured) with the numerical approach (as you helped me with here).
And the outcome will be two linear functions essentially graphed right on top of each other.
That seems to clear the assignment, agreed?

 

[haruspex]

she drew a slightly parabolic curve for the 'example graph' in class on the white board.

Since I was not in the class, I cannot say what the drawing meant. Maybe she was illustrating the basic method of plotting a numerical solution, which would in general give some curve.
You did write

The exact numerical solution and the coding solution should agree here.

I was not quite sure what that meant, but I interpreted it as meaning the numerical solution would exactly match the algebraic solution. That would only ever be true for a straight line.

 

[RJLiberator]

Excellent, thank you for your help here!