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**Problem:**Suppose there is a bullet of a given mass in a barrel at some initial position, with some initial volume and pressure of an ideal gas enclosed behind it. Then at some instant the bullet is allowed to accelerate due to the difference in pressures across the bullet. How do you find the equations of motion of the bullet ~ x(t), v(t), a(t) ? (x for position)

**Assumptions:**no friction between the bullet and barrel, and the bullet makes a perfect seal with the barrel. The temperature of the barrel is constant. The amount of gas is constant. Drag forces are negligible.

I can post my attempted solution if you guys want me too.

Thanks,

Austin