In a physics lab experiment, one end of a horizontal spring that obeys Hooke's law is attached to a wall. The spring is compressed x0 = 0.400 m, and a block with mass 0.300 kg is attached to it. The spring is then released, and the block moves along a horizontal surface. Electronic sensors measure the speed v of the block after it has traveled a distance d from its initial position against the compressed spring. The measured values are listed in the table below.

d (m) v (m/s)
0 0
0.05 0.85
0.10 1.11
0.15 1.24
0.25 1.26
0.30 1.14
0.35 0.90
0.40 0.36
A)

The data show that the speed v of the block increases and then decreases as the spring returns to its unstretched length. Explain why this happens, in terms of the work done on the block by the forces that act on it.

The spring force is initially less than friction, so the block decelerates backward. But eventually the spring force increases enough so that it is greater than the force of friction, and the block then slows down (accelerates).
The spring force is initially greater than friction, so the block accelerates forward. But eventually the spring force decreases enough so that it is less than the force of friction, and the block then slows down (decelerates).
The spring force is always greater than friction, so the block accelerates all the time.
The spring force is always less than friction, so the block decelerates all the time.

B) Use the work-energy theorem to derive an expression for v2 in terms of d. Do not substitute the value of x0 into the expression.

Express your answer in terms of some or all of the variables k, m, d, x0, μk, and the acceleration due to gravity g.

v^2(t)=