An air-track cart of mass m1 = 0.14 kg is moving with a speed v0 = 1.3 m/s to the right when it collides with a cart of mass m2 = 0.25 kg that is at rest. Each cart has a wad of putty on its bumper, and hence they stick together as a result of their collision. Suppose the average contact force between the carts is F = 1.5 N during the collision.

(a) What is the acceleration of cart 1? Give direction and magnitude.

(b) What is the acceleration of cart 2? Give direction and magnitude.

(c) How much time does it take for both carts to have the same speed? (Once the carts have the same speed the collision is over and the contact force vanishes.)

(d) What is the final speed of the carts, vf?

(e) Show that m1 v0 is equal to (m1 + m2)vf.