Using energy to predict velocity

This lab was designed to see if we could cause two carts to travel at the same velocity while only being given the spring constant of both springs (red and blue).
We labeled our data according to spring color.

The two formula's we used were:
Ek=1/2*m*v^2
Eel=1/2Kx^2

Red:
K=84
M= 0.55 Kg

Blue:
K=112
M= 0.5422 Kg


Once we had this data, we set a compression to red, of 5 cm, 0.05 M, and then input it into the formula to solve for energy:
Eel=1/2Kx^2
Red=0.5*84*0.05^2
       = 0.105j
and then we set the energy equal to solve for the Blue compression:
blue=0.5*112*x^2
0.105=56x^2
x= 0.043m

To then solve for velocity, we input this data into the formula:
Eel=Ek because inital energy= final energy
so
Both red and blue Eel=0.105 j which means 0.105j=EK
Thus to solve for velocity we input the energy (0.105j) into the Ek position.
 0.105j=1/2*m*v^2
Red:
0.105j=0.5*0.55*v^2
0.105j=0.275*v^2
0.105j/0.275=(0.275*v^2)/0.275
0.381=v^2
v= 0.617m/s

Blue:
0.105j=0.5*0.5422*v^2
0.105j=0.2711*v^2
0.105j/0.2711=(0.2711*v^2)/0.2711
0.387=v^2
       v=0.622m/s


To double check our blue compression data, we input the velocity of red (0.61 m/s) into the formula to find our Ek:

Ek=0.5*0.5422*0.617^2
Ek=.103j

Which when used as part of the Eel=Ek formula means that Eel=.101.
Thus, when we input this into the Eel formula, we solved for the compression of x for blue.
 Eel=1/2*k*x^2
.103=0.5*112*x^2
.103=56*x^2
.103/56=(56*x^2)/56
 .0018=x^2
 0.0424=x

When we tested the carts, we pulled the cart with the red spring 0.05m (5 cm) back, and the cart with the blue spring back 0.042m (4.2 cm).
We used pasco as our testing software, and our red cart came in at 0.56 m/s for velocity, while the blue cart came in at 0.61 m/s for velocity.
This resulted in a percentage of error for our red cart of (error %=(0.61-0.56)/0.61) 8.1% error.