A particle of mass m kept at the origin is subjected to a froce `vecF=(pt-qx)hati` where t is the time elapsed and x is the x co-ordinate of the position of the particle. Particle starts its motion at t=0 with zero initial velocity. If p and q are positive constants, then:

A particle of mass m is subjected to a force vecF=F_(0)[cos (t)hati+sin(1)hatj] . If initially (t=0) the particle was at rest, the kinetic energy of the particle as a function of time is given by:

A particle of mass m is subject to a force (F) .Find the time dependent position x(t) of the particle for the following two cases : (a) F(x)=kx, with k>0, the initial position is x_(0) , and the initial speed is zero. (b) F(v)=-bv^(2) and the initial position is zero,and the initial speed is v_(0) .

A particle starts from the origin at time t = 0 and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time t = 5s ?

A particle starts from the origin at time t = 0 and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time t = 5s ?

A particle of charge q and mass m is subjected to an electric field E=E_(0)(1-ax^(2)) in the x - direction, where a and E_(0) are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :

A particle of charge q and mass m is subjected to an electric field E=E_(0)(1-ax^(2)) in the x - direction, where a and E_(0) are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :

The position of a particle is given by x=2(t-t^(2)) where t is expressed in seconds and x is in metre. The maximum value of position co-ordinate of particle on positive x -axis is

The position of a particle is given by x=2(t-t^(2)) where t is expressed in seconds and x is in metre. The maximum value of position co-ordinate of particle on positive x -axis is