Position vs. Time graph equation

Click For Summary
SUMMARY

The discussion centers on the derivation of acceleration from a position vs. time graph created during a physics lab on free fall. The participant utilized a spark timer to collect data, resulting in a polynomial fit of the form y(t) = at² + bt + c, where 'a' represents the coefficient of the x² term. To determine acceleration, the participant multiplied the x² coefficient by 2, aligning with the kinematic equation for uniformly accelerated motion, which states that acceleration is equal to twice the coefficient of the squared time term in the polynomial fit.

PREREQUISITES
  • Understanding of kinematic equations in physics
  • Familiarity with polynomial regression analysis
  • Knowledge of free fall motion and gravity
  • Experience with data collection using spark timers
NEXT STEPS
  • Study the derivation of kinematic equations for uniformly accelerated motion
  • Learn about polynomial regression techniques in data analysis
  • Explore the principles of free fall and gravitational acceleration
  • Investigate the use of spark timers in experimental physics
USEFUL FOR

Students in physics courses, educators teaching kinematics, and anyone interested in understanding the relationship between position, time, and acceleration in motion experiments.

lcary
Messages
6
Reaction score
0
I just completed a lab on the acceleration due to gravity and I have to answer a few questions about my data. Before I share what I am confused about I will give a quick run through of the lab procedures:

--First I used a spark timer to mark a strip of paper with a clamp attached to it and let the strip free fall. Then I measured the distance of each mark made from the spark timer with a 2m stick and made a distance vs time graph from the data. I made a best fit polynomial line of degree 2 and found the equation of the fit line that turned out to have the form ___x^2+___x+___, where the ___ is where my coefficients are. I multiplied the x^2 coefficient by 2 to get acceleration.

One of the lab follow up questions asked me why I multiply that coefficient by 2 to get acceleration and I am totally stumped.

Can someone explain why multiplying by 2 gives accel?
thanks
 
Physics news on Phys.org
In your polynomial fit, x represents time (independent variable) and position is y (dependent variable). You fitted coefficients a, b and c to the equation

y(t) = at2 + bt + c.

What kinematic equation gives y(t)? Compare the coefficients between what you know to be the case and what you fitted.
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
View full post »

Similar threads

Voltage vs Distance graph for a given E vs D graph
  • · Replies 9 ·
Replies
9
Views
484
Why would this be accelerating positively?
  • · Replies 6 ·
Replies
6
Views
1K
Finding acceleration from Velocity vs Position graph
  • · Replies 2 ·
Replies
2
Views
4K
Obtaining Acceleration from Position vs Time graph
  • · Replies 3 ·
Replies
3
Views
5K
Position in Velocity-Time Graphs
  • · Replies 1 ·
Replies
1
Views
1K
Acceleration from x vs. t graph
  • · Replies 7 ·
Replies
7
Views
4K
What is the intersection point of two objects on a position vs time graph?
  • · Replies 10 ·
Replies
10
Views
2K
Slope of position vs time squared graph?
  • · Replies 2 ·
Replies
2
Views
13K
Solving Distance Traveled Using Formulas vs. Graphs
  • · Replies 6 ·
Replies
6
Views
2K
Acceleration vs. Time graph confusion
  • · Replies 1 ·
Replies
1
Views
2K