Final answer:
The speed of the block, calculated using conservation of energy principles, does not match any of the given options, indicating a possible error in the provided choices. The correct method involves equating the potential energy of the compressed spring to the kinetic energy of the block.
Step-by-step explanation:
To determine the speed of the block when it has moved a distance of 0.0200 m from its initial position, we need to use conservation of energy, since the surface is frictionless, and therefore, no energy is lost to friction. The potential energy stored in the spring when it is compressed is converted into kinetic energy of the block as it moves.
The potential energy (PE) of the compressed spring is given by the formula PE = (1/2)kx^2, where 'k' is the spring constant and 'x' is the compression distance. When the spring is compressed by 0.0150 m, the potential energy is:
PE = (1/2)(100 N/m)(0.0150 m)^2
PE = 0.01125 J
The kinetic energy (KE) of the block when it has moved 0.0200 m is equal to this potential energy, since energy is conserved. Thus, KE = PE, and we can write:
KE = (1/2)mv^2
0.01125 J = (1/2)(0.200 kg)v^2
After solving for 'v', we find that the speed of the block is:
v = √(2 * 0.01125 J / 0.200 kg)
v = 0.75 m/s
Note that this speed does not match any of the options given in the multiple choice, suggesting there might have been a miscalculation in the question or the choices provided might be incorrect. However, the method to calculate the speed is as described here using conservation of energy principles.