Help with Displacement vs. time and acceleration

[lmn]

Homework Statement

I have the following points that were gathered from a displacement vs. time graph (the graph is of a ball being dropped from rest). The line is parabolic. The quadratic regression for the points is $$-4.03x^2-2.06x+1.20$$ where $$R^2=0.99857$$.

Correct me if I'm wrong but the quadratic regression is the same as this: $$h(t)= \frac {1}{2}At^2+V_{0}t+h_{0}$$

I need to make a velocity vs. time graph with this information but I need a little guidance.

(time (s), displacement (m))
(0.000, 1.194)
(0.097, 0.979)
(0.129, 0.881)
(0.161, 0.774)
(0.193, 0.654)
(0.258, 0.399)
(0.290, 0.254)
(0.322, 0.102)
(0.354, 0.000)

Homework Equations

$$h(t)= \frac {1}{2}At^2+V_{0}t+h_{0}$$

The Attempt at a Solution

I performed the quadratic regression but now I'm stuck

 

[kuruman]

Think of x as representing time t, then match whatever constants you found from your quadratic regression to the constants in the kinematic equation that you quoted. But (and this is a big "but") if the ball was dropped from rest, then the linear term in t must have its coefficient constrained to be zero for a meaningful fit (i.e. v₀=0). I think you need to redo your regression with that in mind. You should be able to predict from the kinematic equation what the fitted parameters ought to be and then verify that they are what you expected.

 

[tomcue]

on how to use this information to create a velocity vs. time graph.

Great job on performing the quadratic regression and obtaining a high R^2 value! This indicates that the quadratic equation is a good fit for the data points and can be used to accurately describe the motion of the ball.

To create a velocity vs. time graph, you will first need to find the velocity at each time point. This can be done by taking the derivative of the displacement vs. time equation, which will give you the velocity vs. time equation: v(t) = At + V0.

Next, you can plug in the time values from the given data points into the velocity equation to calculate the corresponding velocities. Once you have these values, you can plot them on a velocity vs. time graph.

Keep in mind that the velocity vs. time graph will also be parabolic, as the velocity is changing at a constant rate due to the acceleration of gravity. The graph will start at V0 (initial velocity) and decrease as the ball accelerates towards the ground.

I hope this helps guide you in creating your velocity vs. time graph. Remember to always double check your calculations and make sure they make sense in the context of the problem. Good luck with your homework!