A particle is moving along the x-axis. Its position as a function of time is given as x=bt-ct^2a) What must be the units of the constants b and c, if x is in meters and t in seconds?b) At time zero, the particle is at the origin. At what later time t does it pass the origin again?c) Derive an expression for the x-component of velocity. d) At what time t is the particle momentarily at rest?e) Derive an expression for the x-component of the particles acceleration, ax

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants