An air-track cart of mass 0.10 is moving with a speed 1.2 to the right when it collides with a cart of mass 0.24 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 1.3N during the collision. Cart 1 has an acceleration of 13 m/s^2. Cart 2 is accelerating at 5.4 m/s^2.

How long 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.)

What is the final speed of the carts, ?

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  1. The mass of cart 1 is F/a1 = 0.1 kg
    The mass of cart 2 is F/a2 = 0.241 kg
    The final speed Vf of both carts at the end of the collision is given by momentum conservation:
    0.341 Vf = 0.1*1.2
    Vf = 0.352 m/s
    The time required for cart 1 to go from 1.2 m/s to 0.341 m/s while decelerating at 13 m/s^2 is
    0.0682 s.

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