W = 1/2k*x^2.
k = spring constant = 2500 n/m.
x = distance = 4 cm = 0.04m (convert to same units).
W = 1/2(2500)(0.04)^2 = 2J.
The volume of the gas is 
Explanation:
At standard temperature and pressure (stp), the volume occupied by 1 mole of an ideal gas is always equal to

In this problem, we have an amount of moles of gas of
n = 0.034 mol
Since 1 mol of gas occupies a volume of 22.4 L, we can set up the following ratio:

where V is the volume occupied by 0.034 mol of gas. Solving for V, we find

Or, in cubic metres,

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The impulse is equal to the variation of momentum of the object:

where m is the mass object and

is the variation of velocity of the object.
The ball starts from rest so its initial velocity is zero:

. So we can rewrite the formula as

or

and since we know the impulse given to the ball (I=16 Ns) and its mass (m=2 kg), we can find the final velocity of the ball: