Consider an object moving along a line with the following velocity and initial position. v (t )equals6 minus 2 t on [0,5]; s(0)equals0 Determine the position function for tgreater than or equals0 using both the antiderivative method and the Fundamental Theorem of Calculus. Check for agreement between the two methods.

During the experiment if you could triple the breakaway magnetic force with all other quantities left unchanged, what is the new value for the critical velocity if it was v0 (initial velocity), initially? (b) now if you halved the radius with all other quantities left unchanged, what is the new critical velocity if it was v0 (initial velocity), initially? (c) if during the experiment, critical velocity quadrupled with all other quantities left unchanged, what is the new breakaway force if its magnitude was initially f0,?

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

Ahockey player of mass 82 kg is traveling north with a velocity of 4.1 meters per second he collides with the 76 kg player traveling east at 3.4 meters per second if the two players locked together momentarily in what direction will they be going immediately after the collision how fast will they be moving