Obtainwork energy theorem of a particle moving in one dimension under the variable force .

The distance x of a particle moving in one dimensions, under the action of a constant force is related to time t by the equation, t=sqrt(x)+3 , where x is in metres and t in seconds. Find the displacement of the particle when its velocity is zero.

The displacement x of particle moving in one dimension, under the action of a constant force is related to the time t by the equation t = sqrt(x) +3 where x is in meters and t in seconds . Find (i) The displacement of the particle when its velocity is zero , and (ii) The work done by the force in the first 6 seconds .

Obtain the equation of work by variable force in one dimension .

(x, t), (y, t) diagram of a particle moving in 2-dimensions If the particle has a mass of 500 g, find the force (direction and magnitude) acting on the particle.

Derive the work energy theorem for a variable force exerted on a body in one dimension .

Consider the following sketch of potential energy for a particle as a function of position. There are no dissipative forces or internal sources of energy. What is the minimum total mechanical energy that the particle can have if you know that it has travelled over the entire region of X shown?

The centripetal force on a particle moving in a uniform circular motion on a horizontal circle of radius r is (-sigma)/(r^(2)) , then find the mechanical energy of this particle .

The potential energy U(x) of a particle moving along x- axis is shown in figure. Which one of the following graphs represents the variation of kinetic energy of this particle if its total mechanical enery is E_(0)

The relation between position and time f for a particle , performing one dimensional motion is as under : t = sqrt(x) +3 Here x is in metre and t is in second . (1) Find the displacement of the particle when its velocity becomes zero . (2) If a constant force acts on the particle , find the work done in first 6 second .

Given in figure are examples of some potential energy functions in one dimension. The total energy of the aprticle is indicated by a cross on the ordinate axis . In each case , specify the regions ,if any , in which the particle cannot be found for the given energy .Also , indicate the minimum total energy the particle must have in each case . Think of simple physical contexts for which these potential energy shapes are relvant .