Describing the Relationship Between a Parabolic Position vs Time Graph and a Linear Velocity vs Time Graph

[Hckyplayer8]

Hello everyone. I hope all is well. I am finishing up a Physics course and I'm struggling to articulate a decent paragraph about the subject title. What would be the mathematical way of explaining the aforementioned relationship?

Thank you.

 

[lev888]

Hello everyone. I hope all is well. I am finishing up a Physics course and I'm struggling to articulate a decent paragraph about the subject title. What would be the mathematical way of explaining the aforementioned relationship?

Thank you.

The 2 graphs are describing the movement of the same object? Then think about the relationship between the functions of position and velocity.

 

[HallsofIvy]

Velocity is the rate of change of position- i.e. the derivative of the position function. If the position is proportional to t^2 then the velocity is necessarily proportional to 2t.

 

[Hckyplayer8]

The 2 graphs are describing the movement of the same object? Then think about the relationship between the functions of position and velocity.

Velocity is the rate of change of position- i.e. the derivative of the position function. If the position is proportional to t^2 then the velocity is necessarily proportional to 2t.

Thank you for replying. Is there a more elegant to say that while velocity increases at a constant rate (thus linearly), position is a parabolic curve because the distance traveled between intervals increases as the velocity increases?

Also, the position vs time curve looks like an exponential curve. Is it? If so, I thought exponential functions had the variable as an exponent.

 

[JeffM]

They look similar only because you are graphing only part of a parabola.