How Do You Calculate Acceleration from Position and Time Data?

[CustardPi]

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 Y_n+1 - Y_n = V_nt + (1/2)a_yt² 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

Y_n+1 - Y_n = V_nt + (1/2)a_yt²

The Attempt at a Solution

Here's one attempt I tried.

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

a_y = 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.

 

[rl.bhat]

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.

 

[CustardPi]

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?

 

[rl.bhat]

Wright three equators. From the first equation we get Vo = 7-1/2*a. Use this value in other two equations to find a

 

[CustardPi]

Thank you for your help, I figured it out earlier today, things are making more sense every day!