Imagine that a proton released at rest from point A moves in response to the electric field of a fixed charge distribution along a path that takes it through point B. If the potential has a value of 3500 V at A and -1500 V at B, what is the proton's speed as it passes point B

An incident ray through the focal point of a spherical mirror will: reflect through the center of curvature. reflect back through the focal point. reflect parallel to the principle axis. reflect the same direction as the incident ray.

Aparticle moves in the xy plane with constant acceleration. at time zero, the particle is at x = 6 m, y = 8.5 m, and has velocity ~vo = (9 m/s) ˆı + (−2.5 m/s) ˆ . the acceleration is given by ~a = (4.5 m/s 2 ) ˆı + (3 m/s 2 ) ˆ . what is the x component of velocity after 3.5 s? answer in units of m/s.

The atoms in a nickel crystal vibrate as harmonic oscillators with an angular frequency of 2.3 × 1013 rad/s. the mass of a nickel atom is 9.75 × 10-26 kg. what is the difference in energy between adjacent vibrational energy levels of nickel? (h = 6.626 × 10-34 j • s, , 1 ev = 1.60 × 10-19 j)