Two air-track carts, one on the left with mass 100g and one on the left with mass 300g) are sliding to the right at 1.0 m/s. There is a spring between them that has a spring constant of 100N/m and is compressed 4.2 cm. There is a string that holds the two carts together. The carts slide past a flame that burns through the string holding them together. (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!