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(After the flame burns the string)...

Q1: What is the speed of 100g cart?

Q2: What is the direction of the motion of 100g cart? I got to the left

Q3:What is the speed of 300g cart?

Q4:What is the direction of the motion of 300g cart? I got to the right

Here is how I started off for Q1 and Q3:

F=-k[tex]\Delta[/tex]s

F=(100)(.042) = 4.2 N

@Q1 I drew my force diagram, so the force by the spring on the 100g block points in the negative direction, so I got:

[tex]\sum[/tex]Fx = -Fspring = ma

-4.2N = (.1kg)(acceleration)

acceleration = -42m/s^2

Then, I used kinematics to solve for final velocity (vf)

Vf^2 = Vi^2 + 2a[tex]\Delta[/tex]s

since the spring is compressed 4.2cm, then the distance for it to return to equilibrium is .021m on each side...so

Vf^2 = 1^2 +2(-42)(.021)

vf^2=-.764

Now I'm stuck, because I don't want to take the square root of a negative...which makes me think I've done something wrong.

I will follow the same procedure for Q3...once I figure out what I'm doing wrong in Q1.

Please help me where I've messed up.

Thanks!