How Do You Calculate Acceleration from Position and Time Data?

AI Thread Summary
To calculate acceleration from position and time data, the equation Yn+1 - Yn = Vnt + (1/2)ayt² is used, where Yn represents position, Vn is initial velocity, and ay is acceleration. The user initially struggles with determining initial velocity, which is not provided, leading to confusion in solving for acceleration. By setting up equations for different position points, they can derive initial velocity and subsequently solve for acceleration. After multiple attempts, the user successfully figures out the calculations, indicating progress in understanding the concept. The discussion highlights the importance of correctly applying kinematic equations in physics problems.
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Ok, I've been running over this problem for about an hour now, and I can't figure out where I'm going wrong. I'm a complete newb, so I'm sure it's something stupid, but I could use the help.

Homework Statement


An object with an initial velocity undergoes constant acceleration. Position information was collected at 4 poins and is shown in the table. Using Yn+1 - Yn = Vnt + (1/2)ayt2 determine the acceleration and fill in each box.

edit : it screwed up my table, I hope it makes sense.

Point #; Time (s); Position (m); Average Acceleration (m/s2
1; 0; 1; n/a
2; 1; 8; (answer here)
3; 2; 25; (answer here)
4; 3; 52; n/a

Homework Equations



Yn+1 - Yn = Vnt + (1/2)ayt2

The Attempt at a Solution



Here's one attempt I tried.

25m - 8m = 7(1) + 1/2ay(1)

ay = 20

I've tried a few different attempts, I'm not sure I should show them all here. The problem I'm running into is that I think I need to plug in velocity figures, but I wasn't given any, so I messed around some, but the answers don't make sense, and aren't uniform.
 
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At position 1 Yn = 1m, and Vn is the initial velocity.
At position 2 Yn+1 = 8 m and t = 1s
At position 3 Yn+1 = 25 m and t = 2s
At position 4 Yn+1 = 52 m and t = 3s
From position 1 and 2 you get 8-1 = V0 +1/2*a...(1) Similarly wright the equations for positions 1 and 3, and 1 and 4. Solve the equations to find the acceleration.
 
Last edited:
Ok, that all makes sense, but I'm still not sure what to do for initial velocity, since it wasn't given to us. Am I supposed to use some equation to find it?
 
Wright three equators. From the first equation we get Vo = 7-1/2*a. Use this value in other two equations to find a
 
Thank you for your help, I figured it out earlier today, things are making more sense every day!
 
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