A mass of 4.0 kg is in motion along a horizontal, frictionless surface with a speed of 2.5 m/s when it makes contact with a horizontal spring anchored to a wall. The spring compresses and brings the mass to a momentary rest. The spring constant is 1250 N/m. a) Determine the maximum distance the spring is compressed. b) Determine the speed of the block when the spring is compressed a distance of 9.5 cm.

Simply use conservation of energy

The initial energy is purely kinetic: 0.5mv2

When the spring is compressed to the max, the energy is purely potential: 0.5kx2

When the spring is partially compressed, the energy is a mixture of both: 0.5mv2+0.5kx2

Since the energy is a constant at every step of the way, you can equate the initial energy to the maximum potential energy and isolate x to find the maximum compression, then, for a known compression, you can equate the total energy to the third equation I wrote and isolate the final velocity

1.   what is light?

light is an electromagnetic wave visible to the human eye. 

2. what is a reflection?

the rebounding of a light ray when it hits a mirror.

3. what is the incident ray?

contacts the surface of an object.

4. what is the reflected ray?

bounces off a reflective surface.

5. what is the normal ray?

perpendicular to the surface of a mirror.

6. what is the angle of incidence?

an angle formed by the incident ray and the normal.

7. what is the angle of reflection?

an angle formed by the reflected ray and the normal.

8. what is refraction?

(bending.)

9. what is a converging lens?

bring together light rays that pass through.

10. what is a diverging lens?

spreads out light passing through.

11. focal point?

the real point where the refracted rays meet when the incident rays run parallel.

i copy pasted btw from an website..