# A spring with a constant of #3 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #4 kg# and speed of #6 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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To find the compression of the spring, you can use the conservation of mechanical energy formula: ( \frac{1}{2}kx^2 = \frac{1}{2}mv^2 ), where ( k ) is the spring constant, ( x ) is the compression of the spring, ( m ) is the mass of the object, and ( v ) is the velocity of the object.

Plugging in the given values: ( k = 3 , \text{kg/s}^2 ), ( m = 4 , \text{kg} ), and ( v = 6 , \text{m/s} ),

( \frac{1}{2}(3 , \text{kg/s}^2)x^2 = \frac{1}{2}(4 , \text{kg})(6 , \text{m/s})^2 )

( 3x^2 = 4 \times 36 )

( 3x^2 = 144 )

( x^2 = \frac{144}{3} )

( x^2 = 48 )

( x = \sqrt{48} )

( x \approx 6.93 , \text{m} )

Therefore, the spring will compress approximately ( 6.93 , \text{m} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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